An analytic model is presented for the description of the motion of a charged particle in the interaction of an elliptically electromagnetic pulse polarizedpropagating along a static and homogeneous external magnetic field in a plasma starting from the force equation. The method allows to express the solution in terms of the invariant phase, obtaining differential equations for the trajectory of the accelerated particle by means of an electromagnetic pulse of arbitrary and modulated width by an encircling Gaussian. The numerical solutions reported in this work can find varied applications, for example in the physics of the interaction laser-plasma, in the acceleration of particles, in hot plasma and in radioactive effects. (Author)

An analytical model for the description of the movement of a charged particle in the interaction of an electromagnetic pulse ellipticallypolarizedpropagating along of a static and homogeneous external magnetic field in a plasma starting from the force equation is presented. The method allows to express the solution in terms of the invariant phase, obtaining differential equations for the trajectory of the accelerated particle by means of an electromagnetic pulse of arbitrary amplitude and modulated by an encircling Gaussian. The numerical solutions reported in this work can find varied applications, for example in the physics of the interaction laser-plasma, in the acceleration of particles, in hot plasma and in radiative effects. (Author)

ECH experiments on PLT with resonance frequencies of 80 to 90 GHz at the plasma center use 60 GHz extraordinary mode (X-mode) propagation at 30 0 from the toroidal field. Efficient excitation of this mode requires ellipticpolarization of the incident wave at the plasma edge. On PLT the ellipticpolarization is achieved outside the vacuum vessel in an elliptically deformed section of circular waveguide propagating TM11, a mode that is intermediate between TE01 and HE11 (which has an ideal radiation pattern). The squeeze and orientation of the TM11 polarizer are adjusted to compensate both for the birefringence of a corrugated bend propagating HE11 and for a flat mirror inside PLT that reverses the sense of rotation of the polarization. 11 refs., 8 figs

Measurements of orthogonal, horizontal components of the magnetic field in the ELF range obtained during September 1985 show that the Schumann resonance eigenfrequencies determined separately for the north-south and east-west magnetic components differ by as much as 0.5 Hz, suggesting that the underlying magnetic signal is not linearly polarized at such times. The high degree of magnetic ellipticity found suggests that the side multiplets of the Schumann resonances corresponding to azimuthally inhomogeneous normal modes are strongly excited in the highly asymmetric earth-ionosphere cavity. The dominant sense of polarization over the measurement passband is found to be right-handed during local daylight hours, and to be left-handed during local nighttime hours. 16 references

A superconducting, ellipticallypolarized undulator (SEPU24) with a period of length 24 mm was developed to provide first-harmonic photons from a 0.8 GeV storage ring for extreme-ultraviolet (EUV) lithography experiment. In SEPU24, two layers of a magnet array structure - with and without rotated magnet arrays - are combined to generate a helical field that provides radiation with wavelength 13.5 nm in the in-band energy. The arrays of iron and aluminium poles were wound with a racetrack coil vertically as for the magnet pole array. The elliptical field is created when the up and down magnet-pole arrays pass excitation currents in alternate directions. SEPU24 is designed with a magnet of gap 6.8 mm, yielding magnetic flux density B x =B z =0.61 T of the helical field. A prototype magnet was fabricated with a diode for quench protection, and assembled in a test dewar to test the magnet performance. A cryogenic Hall-probe system with a precise linear stage was used to measure the distribution of the magnetic field. We describe the design concept and algorithm, the engineering design, the calculation of the magnetic field, the construction and testing of the 10-pole prototype magnet and related issues.

The effect of ground reflections upon the far field of an ellipticallypolarized antenna of ar itrary orientation with r spect to ground is...investigated. The equation of the polarization ellipse produced by an ellipticallypolarized antenna in the presence of ground is derived, AND SEVERAL...EXAMPLES ILLUSTRATE THE VARIATION IN THE AXIS RATIO OF THE POLARIZATION ELLIPSE AS A FUNCTION OF THE GEOMETRY OF THE MEASURING SETUP. A method is presented

The theoretical investigation results of disintegration effect of ellipticpolarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed ellipticpolarized control field and in weak probe field approximation are presented. It is shown that this disintegration occurs because the probe field in the medium is the sum of two normal modes, which correspond to ellipticpolarized pulses with different speeds of propagation. The polarization ellipses of normal modes have equal eccentricities and mutually perpendicular major axes. Major axis of polarization ellipse of one normal mode is parallel to polarization ellipse major axis of control field, and electric vector of this mode rotates in the opposite direction, than electric vector of the control field. The electric vector other normal mode rotates in the same direction that the control field electric vector. The normal mode speed of the first type aforementioned is less than that of the second type. The polarization characteristics of the normal mode depend uniquely on the polarization characteristics of ellipticpolarized control field and remain changeless in the propagation process. The theoretical investigation is performed for Λ-scheme of degenerated quantum transitions between 3P0, 3P10 and 3P2 energy levels of 208Pb isotope.

We propose a novel optical asymmetric image encryption method based on amplitude reconstruction of ellipticallypolarized light, which is free from silhouette problem. The original image is analytically separated into two phase-only masks firstly, and then the two masks are encoded into amplitudes of the orthogonal polarization components of an ellipticallypolarized light. Finally, the ellipticallypolarized light propagates through a linear polarizer, and the output intensity distribution is recorded by a CCD camera to obtain the ciphertext. The whole encryption procedure could be implemented by using commonly used optical elements, and it combines diffusion process and confusion process. As a result, the proposed method achieves high robustness against iterative-algorithm-based attacks. Simulation results are presented to prove the validity of the proposed cryptography.

A scalar variational analysis based on a Gaussian approximation of the fundamental mode of a double-clad elliptical fiber with a depressed inner cladding is studied. The polarization properties and graphic results are presented; they are given in terms of three parameters: the ratio of the major axis to the minor axis of the core, the ratio of the inner cladding major axis to the core major axis, and the difference between the core index and the inner cladding index. The variations of both the spot size and the field intensity with core ellipticity are examined. It is shown that high birefringence and dispersion-free orthogonal polarization modes can be obtained within the single-mode region and that the field intensity distribution may be more confined to the fiber center than in a single-clad elliptical fiber.

When ellipticallypolarized light of appropriate wavelength Corresponding to trans-cis-trans isomerisation process is incident on thin films of azobenzene polyesters, a helical structure is induced. We investigate the propagation of the exciting light beam (self-induced) as well as a probe light...... beam outside the absorption band through the polyester films. Investigations are carried out in one amorphous and one liquid crystalline polyester. We show that amorphous polyester after irradiation behaves like classical helical material....

We demonstrate, theoretically and experimentally, that an intense, ellipticallypolarized, nonresonant laser field can simultaneously force all three axes of a molecule to align along given axes fixed in space, thus inhibiting the free rotation in all three Euler angles. Theoretically, the effect...

Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compared to the outcome of trajectory simulations.

The generation of ellipticallypolarized electromagnetic wave of an antiferromagnetic (AF)/dielectric sandwiched structure in the terahertz range is studied. The frequency and external magnetic field can change the AF optical response, resulting in the generation of ellipticalpolarization. An especially useful geometry with high levels of the generation of ellipticalpolarization is found in the case where an incident electromagnetic wave perpendicularly illuminates the sandwiched structure, the AF anisotropy axis is vertical to the wave-vector and the external magnetic field is pointed along the wave-vector. In numerical calculations, the AF layer is FeF2 and the dielectric layers are ZnF2. Although the effect originates from the AF layer, it can be also influenced by the sandwiched structure. We found that the ZnF2/FeF2/ZnF2 structure possesses optimal rotation of the principal axis and ellipticity, which can reach up to about thrice that of a single FeF2 layer.

Nonlinear quantum-mechanical phenomena in strong laser fields, such as high-order harmonic generation (HHG) and above-threshold ionization (ATI) are significantly modified if the applied laser field is bichromatic and/or ellipticallypolarized. Numerical results obtained within the strong-field approximation are presented for two special cases. We show results for HHG by plasma ablation in a bichromatic linearly polarized laser field. We also consider the ATI process in bicircular field which consists of two coplanar counter-rotating circularly polarized fields.

When a molecule with an anisotropic polarizability is placed in a strong nonresonant laser field the interaction occurs through the induced dipole moment. The outcome is that the molecule experiences an angular dependent potential energy. It is now well established that a linearly polarized laser...... field can be used to align molecules along their axis of highest polarizability. Here we demonstrate, theoretically and experimentally, that an ellipticallypolarized laser field can be used to simultaneously force two axes of a molecule into alignment through the same mechanism. Due to the rigidity...

A recent paper reported ellipticallypolarized high-order harmonics from aligned N2 using a linearly polarized driving field [X. Zhou et al., Phys. Rev. Lett. 102, 073902 (2009)]. This observation cannot be explained in the standard treatment of the Lewenstein model and has been ascribed to many...

An analytical model for the description of the movement of a charged particle in the interaction of an electromagnetic pulse ellipticallypolarizedpropagating along of a static and homogeneous external magnetic field in a plasma starting from the force equation is presented. The method allows to express the solution in terms of the invariant phase, obtaining differential equations for the trajectory of the accelerated particle by means of an electromagnetic pulse of arbitrary amplitude and modulated by an encircling Gaussian. The numerical solutions reported in this work can find varied applications, for example in the physics of the interaction laser-plasma, in the acceleration of particles, in hot plasma and in radiative effects. (Author)

An analytic model is presented for the description of the motion of a charged particle in the interaction of an elliptically electromagnetic pulse polarizedpropagating along a static and homogeneous external magnetic field in a plasma starting from the force equation. The method allows to express the solution in terms of the invariant phase, obtaining differential equations for the trajectory of the accelerated particle by means of an electromagnetic pulse of arbitrary and modulated width by an encircling Gaussian. The numerical solutions reported in this work can find varied applications, for example in the physics of the interaction laser-plasma, in the acceleration of particles, in hot plasma and in radioactive effects. (Author)

Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell's equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method

We explore ionization and rescattering in strong mid-infrared laser fields in the nondipole regime over the full range of polarizationellipticity. In three-dimensional photoelectron momentum distributions (3D PMDs) measured with velocity map imaging spectroscopy, we observe the appearance of a sharp ridge structure along the major polarization axis. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with ellipticallypolarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. These ridge electrons are directly related to a counterintuitive shift of the PMD peak opposite to the laser beam propagation direction when the dipole approximation breaks down. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.

The authors present a planar helical undulator designed to produce ellipticallypolarized light. Helical magnetic fields may be produced by a variety of undulators with four parallel cassettes of magnets. In their design, all cassettes are mounted in two planes on slides so that they may be moved parallel to the electron beam. This allows the undulator to produce x-rays of left- or right-handed elliptical or circular polarization as well as horizontal or vertical linear polarization. In model calculations, they have found that by sliding the top pair of rows with respect to the bottom pair, or the left pair with respect to the right pair, they retain the polarization setting but change the magnetic field strength, and hence the x-ray energy. This allows them to select both energy and polarization by independent phase adjustments alone, without changing the gap between the rows. Such a design may be simpler to construct than an adjustable gap machine. The authors present calculations that model its operation and its effects on an electron beam

We study the propagation of plane electromagnetic waves through different systems consisting of arrays of split rings of different orientations. Many extraordinary EM phenomena were discovered in such systems, contributed by the off-diagonal magnetoelectric susceptibilities. We find a mode such that the electric field becomes ellipticallypolarized with a component in the longitudinal direction (i.e. parallel to the wavevector). Even though the group velocity [Formula: see text] and the wavevector k are parallel, in the presence of damping, the Poynting vector does not just get 'broadened', but can possess a component perpendicular to the wavevector. The speed of light can be real even when the product ϵμ is negative. Other novel properties are explored.

The present study deals with the control of a Mach 2 elliptic jet from a convergent–divergent elliptic nozzle of aspect ratio 4 using tabs at the nozzle exit. The experiments were carried out for rectangular and triangular tabs of the same blockage, placed along the major and minor axes of the nozzle exit, at different levels of nozzle expansion. The triangular tabs along the minor axis promoted superior mixing compared to the other controlled jets and caused substantial core length reduction at all the nozzle pressure ratios studied. The rectangular tabs along the minor axis caused core length reduction at all pressure ratios, but the values were minimal compared to that of triangular tabs along the minor axis. For all the test conditions, the mixing promotion caused by tabs along the major axis was inferior to that of tabs along the minor axis. The waves present in the core of controlled jets were visualized using a shadowgraph. Comparison of the present results with the results of a controlled Mach 2 elliptic jet of aspect ratio 2 (Aravindh Kumar and Sathakrishnan 2016 J. Propulsion Power 32 121–33, Aravindh Kumar and Rathakrishnan 2016 J. Aerospace Eng. at press (doi:10.1177/0954410016652921)) show that for all levels of expansion, the mixing effectiveness of triangular tabs along the minor axis of an aspect ratio 4 nozzle is better than rectangular or triangular tabs along the minor axis of an aspect ratio 2 nozzle. (paper)

The present study deals with the control of a Mach 2 elliptic jet from a convergent–divergent elliptic nozzle of aspect ratio 4 using tabs at the nozzle exit. The experiments were carried out for rectangular and triangular tabs of the same blockage, placed along the major and minor axes of the nozzle exit, at different levels of nozzle expansion. The triangular tabs along the minor axis promoted superior mixing compared to the other controlled jets and caused substantial core length reduction at all the nozzle pressure ratios studied. The rectangular tabs along the minor axis caused core length reduction at all pressure ratios, but the values were minimal compared to that of triangular tabs along the minor axis. For all the test conditions, the mixing promotion caused by tabs along the major axis was inferior to that of tabs along the minor axis. The waves present in the core of controlled jets were visualized using a shadowgraph. Comparison of the present results with the results of a controlled Mach 2 elliptic jet of aspect ratio 2 (Aravindh Kumar and Sathakrishnan 2016 J. Propulsion Power 32 121–33, Aravindh Kumar and Rathakrishnan 2016 J. Aerospace Eng. at press (doi:10.1177/0954410016652921)) show that for all levels of expansion, the mixing effectiveness of triangular tabs along the minor axis of an aspect ratio 4 nozzle is better than rectangular or triangular tabs along the minor axis of an aspect ratio 2 nozzle. (paper)

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, ellipticallypolarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused ellipticallypolarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the ellipticallypolarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with ellipticallypolarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

For ellipticallypolarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.

We demonstrate a novel optical asymmetric cryptosystem based on the principle of ellipticalpolarized light linear truncation and a numerical reconstruction technique. The device of an array of linear polarizers is introduced to achieve linear truncation on the spatially resolved ellipticalpolarization distribution during image encryption. This encoding process can be characterized as confusion-based optical cryptography that involves no Fourier lens and diffusion operation. Based on the Jones matrix formalism, the intensity transmittance for this truncation is deduced to perform ellipticalpolarized light reconstruction based on two intensity measurements. Use of a quick response code makes the proposed cryptosystem practical, with versatile key sensitivity and fault tolerance. Both simulation and preliminary experimental results that support theoretical analysis are presented. An analysis of the resistance of the proposed method on a known public key attack is also provided.

We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N 2 , CO 2 , and O 2 molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted with polarization parallel or perpendicular to the direction of the same returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a 'complete' experiment in molecules.

Frozen waves (FWs) are a class of diffraction- and attenuation-resistant beams whose intensity pattern along the direction of propagation can be chosen arbitrarily, thus making them relevant for engineering the spatial configuration of optical fields. To date, analyses of such beams have been done essentially for the scalar case, with the vectorial nature of the electromagnetic fields often neglected. Although it is expected that the field components keep the fundamental properties of the scalar FWs, a deeper understanding of their electromagnetic counterparts is mandatory in order to exploit their different possible polarization states. The purpose of this paper is to study the properties of electromagnetic FWs with radial, azimuthal, linear, circular, and ellipticalpolarizations under paraxial and nonparaxial regimes in nonabsorbing media. An intensity pattern is chosen for a scalar FW, and the vectorial solutions are built after it via the use of Maxwell's equations. The results show that the field components and the longitudinal component of the time-averaged Poynting vector closely follow the pattern chosen even under highly nonparaxial conditions, showing the robustness of the FW structure to parameters variations.

In quantum information, control of the single photon's polarization is essential. Here, we demonstrate single photon generation in a pre-programmed and deterministic polarization state, on a chip-scale platform, utilizing site-controlled elliptical quantum dots (QDs) synthesized by a top-down approach. The polarization from the QD emission is found to be linear with a high degree of linear polarization and parallel to the long axis of the ellipse. Single photon emission with orthogonal polarizations is achieved, and the dependence of the degree of linear polarization on the QD geometry is analyzed.

The dispersion properties of ellipticallypolarized electromagnetic waves in a magnetized electron-positron-pair (EP-pair) plasma are studied with the effects of particle dispersion associated with the Bohm potential, the Fermi degenerate pressure, and the exchange-correlation force. Two possible modes of the extraordinary or X wave, modified by these quantum effects, are identified and their propagation characteristics are investigated numerically. It is shown that the upper-hybrid frequency and the cutoff and resonance frequencies are no longer constants but are dispersive due to these quantum effects. It is found that the particle dispersion and the exchange-correlation force can have different dominating roles on each other depending on whether the X waves are of short or long wavelengths (in comparison with the Fermi Debye length). The present investigation should be useful for understanding the collective behaviors of EP plasma oscillations and the propagation of extraordinary waves in magnetized dense EP-pair plasmas.

Mode separation ratio from an arbitrary ellipticallypolarized electromagnetic wave to an ordinary and an extraordinary modes on a plasma surface for oblique launch is evaluated quantitatively for designing an electron cyclotron current drive (ECCD) antenna. An optimized ellipticalpolarization for the wide range of injection angles and magnetic fields is firstly investigated for ECCD and ECH experiments. (author)

We report a newly discovered anomalous incident-angle of an elastically refracted P-wave, arising from a P-wave impinging on an interface between two VTI media with strong anisotropy. This anomalous incident-angle is found to be located in the post-critical incident-angle region corresponding to a refracted P-wave. Invoking Snell’s law for a refracted P-wave provides two distinctive solutions before and after the anomalous incident-angle. For an inhomogeneously refracted and ellipticallypolarized P-wave at the anomalous incident-angle, its rotational direction experiences an acute variation, from left-hand elliptical to right-hand ellipticalpolarization. The new findings provide us an enhanced understanding of acoustical-wave scattering and lead potentially to widespread and novel applications.

We solve the three-dimensional time-dependent Schrödinger equation and present investigations of the imprint of the orbital angular node in photoelectron momentum distributions of an aligned atomic p-type orbital following ionization by an intense ellipticallypolarized laser pulse of femtosecond...

Full Text Available The potential use of two planar superconducting elliptical undulators—a vertically wound racetrack coil structure and a staggered array structure—to generate a circularly polarized hard x-ray source was investigated. The magnetic poles and wires of the up and down magnet arrays were rotated in alternating directions on the horizontal plane, an elliptical field is generated to provide circularly polarized light in the electron-storage ring and the energy-recovery linac accelerator. Rapid switching between right- and left-circularly polarized radiations is performed using two undulators with oppositely rotated wires and poles. Given a periodic length of 15 mm and a gap of 5 mm, the magnetic-flux densities in the elliptical undulator are B_{z}=1.2 T (B_{x}=0.6 T and B_{z}=0.35 T (B_{x}=0.15 T in the planar vertically wound racetrack coil and the staggered structure with poles rotated by 35° and 25°, respectively. In maximizing the merit of the flux and the width of the effective field region in the two superconducting elliptical undulators, the trade-off rotation angles of the coils and poles are 20° and 5°, for vertically wound racetrack coil and staggered undulators, respectively.

The laser-assisted photoelectric effect in atomic hydrogen is investigated for linear, circular and general ellipticpolarizations. The perturbative dressed state of the atom in an ellipticallypolarized nonresonant laser field is derived in the velocity gauge. The continuum state of the ejected electron is described by a Coulomb-Volkov wavefunction. Numerical results show that the ionization cross section by a vacuum ultraviolet photon is enhanced at high laser field intensities and low frequencies. At small and extremely large scattering angles (measured with respect to the wave vector of the incoming vacuum ultraviolet photon), the process for emitting a laser photon is predominant, while at medium angles, the result favours the process without a laser photon exchange. The dependence of the results on the laser polarization and on various geometries is studied, and an interesting pattern is found for the dependence on the frequency of the dressing laser; an intuitive explanation is offered.

We solve the three-dimensional time-dependent Schroedinger equation and present investigations of the imprint of the orbital angular node in photoelectron momentum distributions of an aligned atomic p-type orbital following ionization by an intense ellipticallypolarized laser pulse of femtosecond duration. We investigate the role of light ellipticity and the alignment angle of the major polarization axis of the external field relative to the probed orbital by studying radial and angular momentum distributions, the latter at a fixed narrow interval of final momenta close to the peak of the photoelectron momentum distribution. In general only the angular distributions carry a clear signature of the orbital symmetry. Our study shows that circular polarization gives the most clear imprints of orbital nodes. These findings are insensitive to pulse duration.

Four-photon double detachment of the helium negative ion is investigated experimentally and theoretically for photon energies where the transient helium atom is in the 1 s 2 s 3S or 1 s 2 p P3o states, which subsequently ionize by absorption of three photons. Ionization is enhanced by intermediate resonances, giving rise to series of peaks in the He+ spectrum, which we study in detail. The He+ yield is measured in the wavelength ranges from 530 to 560 nm and from 685 to 730 nm and for various polarizations of the laser light. Double detachment is treated theoretically as a sequential process, within the framework of R -matrix theory for the first step and effective Hamiltonian theory for the second step. Experimental conditions are accurately modeled, and the measured and simulated yields are in good qualitative and, in some cases, quantitative agreement. Resonances in the double detachment spectra can be attributed to well-defined Rydberg states of the transient atom. The double detachment yield exhibits a strong dependence on the laser polarization which can be related to the magnetic quantum number of the intermediate atomic state. We also investigate the possibility of nonsequential double detachment with a two-color experiment but observe no evidence for it.

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal ellipticallypolarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

Corning has introduced a new polarization-maintaining optical fiber to satisfy customer requirements for a range of commercial and military FOG applications. This fiber has an elliptical core, matched-clad design, and is intended for operation in the 780 to 850 nm wavelength region. The fiber has a beat length less than 1.5 mm, attenuation rate less than 10 dB/km, and a typical coiled h-parameter less than 1.5 X 10-4 m-1 in the designated operating wavelength range. It has a cladding diameter of 80 micrometers and a coating diameter of 185 micrometers . The coating is an acrylate system, similar to that used in telecommunications optical fibers. We report on the performance of this elliptical core fiber for a variety of environmental exposures representative of an automotive application.

When ellipticallypolarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of ellipticallypolarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.

The production of intense isolated attosecond pulse is a major goal in ultrafast research. Recent advances in high harmonic generation from relativistic plasma mirrors under oblique incidence interactions gave rise to photon-rich attosecond pulses with circular or ellipticalpolarization. However, to achieve an isolated elliptical attosecond pulse via polarization gating using currently available long driving pulses remains a challenge, because polarization gating of high harmonics from relativistic plasmas is assumed only possible at normal or near-normal incidence. Here we numerically demonstrate a scheme around this problem. We show that via control of plasma dynamics by managing laser polarization, it is possible to gate an intense single attosecond pulse with high ellipticity extending to the soft X-ray regime at oblique incidence. This approach thus paves the way towards a powerful tool enabling high-time-resolution probe of dynamics of chiral systems and magnetic materials with current laser technology.

Ellipticallypolarized laser fields provide a new channel for access to strong-field processes that are either suppressed or not present under linear polarization. Quantum theory is mostly unavailable for their analysis, and we report here results of a systematic study based on a classical ensemble theory with solution of the relevant ab inito time-dependent Newton equations for selected model atoms. The study's approach is necessarily nonadiabatic, as it follows individual electron trajectories leading to single, double, and triple ionizations. Of particular interest are new results bearing on open questions concerning experimental reports of unexplained species dependences as well as double-electron release times that are badly matched by a conventional adiabatic quantum tunneling theory. We also report the first analysis of electron trajectories for sequential and non-sequential triple ionization.

Metamaterials have been widely applied in the polarization conversion of terahertz (THz) waves. However, common plasmonic metamaterials usually work as reflective devices and have low transmissions. All-dielectric metamaterials can overcome these shortcomings. An all-dielectric metamaterial based on silicon with elliptical air holes is reported to achieve high artificial birefringence at THz frequencies. Simulations show that with appropriate structural parameters the birefringence of the dielectric metamaterial can remain flat and is above 0.7 within a broad band. Moreover, the metamaterial can be designed as a broadband quarter wave plate. A sample metamaterial was fabricated and tested to prove the validity of the simulations, and the sample could work as a quarter wave plate at 1.76 THz. The all-dielectric metamaterial that we proposed is of great significance for high performance THz polarization converters.

Beams with polarization singularities have attracted immense recent attention in a wide array of scientific and technological disciplines. We demonstrate a class of optical fibers in which these beams can be generated and propagated over long lengths with unprecedented stability, even...

Thanks to the superiority in controlling the optical wave fronts, plasmonic nanostructures have led to various striking applications, among which metasurface holograms have been well developed and endowed with strong multiplexing capability. Here, we report a new design of multiplexed plasmonic hologram, which allows for reconstruction of multiple holographic images in free space by scatterings of surface plasmon polariton (SPP) waves in different propagation directions. Besides, the scattered polarization states can be further modulated by arranging the orientations of nanoscatterers. By incorporation of the SPP propagation and polarized scattering, a 4-fold hologram with low crosstalk is successfully demonstrated, which breaks the limitation of only two orthogonal states in conventional polarization multiplexers. Moreover, our design using the near-field SPP as reference wave holds the advantage for compact integration. This holographic approach is expected to inspire new photonic designs with enhanced information capacity and integratability.

In the tunneling regime we present a semiclassical model of above-threshold ionization with inclusion of the Stark shift of the initial state, the Coulomb potential, and a polarization induced dipole potential. The model is used for the investigation of the photoelectron momentum distributions...... in close to circularly polarized light, and it is validated by comparison with ab initio results and experiments. The momentum distributions are shown to be highly sensitive to the tunneling exit point, the Coulomb force, and the dipole potential from the induced dipole in the atomic core...

The room electromagnetics (RE) theory describes the radio propagation in a single room assuming diffuse scat- tering. A main characteristic is the exponential power-delay profile (PDP) decaying with the so-called reverberation time (RT) parameter, depending only on the wall area, the volume...... of the room and an absorption coefficient. The PDP is independent on the location in the room, except for the arrival time. Based on measurements in a room with a spherical array of 16 dual- polarized wideband horn antennas, the current work studies how the RE parameters depend on the receiver (Rx) antenna...

Three sets of a vacuum system were developed and fabricated for ellipticallypolarized undulators (EPU) of a 3-GeV synchrotron facility. These chambers were shaped with low roughness extrusion and oil-free machining; the design combines aluminium and stainless steel. The use of a bimetallic material to connect the EPU to the vacuum system achieves the vacuum sealing and to resolve the leakage issue due to bake process induced thermal expansion difference. The interior of the EPU chamber consists of a non-evaporable-getter strip pump in a narrow space to absorb photon-stimulated desorption and to provide a RF bridge design to decrease impedance effect in the two ends of EPU chamber. To fabricate these chambers and to evaluate the related performance, we performed a computer simulation to optimize the structure. During the machining and welding, the least deformation was achieved, less than 0.1 mm near 4 m. In the installation, the linear slider can provide a stable and precision moved along parallel the electron beam direction smoothly for the EPU chamber to decrease the twist issue during baking process. The pressure of the EPU chamber attained less than 2×10-8 Pa through baking. These vacuum systems of the EPU magnet have been installed in the electron storage ring of Taiwan Photon Source in 2015 May and have normally operated at 300 mA continuously since, and to keep beam life time achieved over than 12 h.

Three sets of a vacuum system were developed and fabricated for ellipticallypolarized undulators (EPU) of a 3-GeV synchrotron facility. These chambers were shaped with low roughness extrusion and oil-free machining; the design combines aluminium and stainless steel. The use of a bimetallic material to connect the EPU to the vacuum system achieves the vacuum sealing and to resolve the leakage issue due to bake process induced thermal expansion difference. The interior of the EPU chamber consists of a non-evaporable-getter strip pump in a narrow space to absorb photon-stimulated desorption and to provide a RF bridge design to decrease impedance effect in the two ends of EPU chamber. To fabricate these chambers and to evaluate the related performance, we performed a computer simulation to optimize the structure. During the machining and welding, the least deformation was achieved, less than 0.1 mm near 4 m. In the installation, the linear slider can provide a stable and precision moved along parallel the electron beam direction smoothly for the EPU chamber to decrease the twist issue during baking process. The pressure of the EPU chamber attained less than 2×10{sup −8} Pa through baking. These vacuum systems of the EPU magnet have been installed in the electron storage ring of Taiwan Photon Source in 2015 May and have normally operated at 300 mA continuously since, and to keep beam life time achieved over than 12 h.

The self-focusing and self defocusing of an elliptically shaped high power laser beam in an extradense plasma is discussed. On account of the ponderomotive force induced by the spatial variation of irradiance in the transverse plane, an electron density gradient is created in the overdense plasma where the beam can penetrate. Self-focusing of the beam in the x and y directions for different critical powers has been extensively studied.

Calculations of Rydberg excitation energies with the second-order polarizationpropagator approximation (SOPPA) often produce results which are more in error than the random phase approximation (RPA), which formally is the first-order model. This is obviously because of cancellation of errors...... at the RPA level. On the other hand, valence excitation energies behave as expected, and they are systematically improved in SOPPA compared to RPA. Note that a Rydberg series is related to one of the ionization thresholds of the molecule, and it is thus obvious that a good description of the ionization...

Ray-tracing of polarized neutrons faces a challenge when the neutron propagates through an inhomogeneous magnetic field. This affects simulations of novel instruments using encoding of energy or angle into the neutron spin. We here present a new implementation of propagation of polarized neutrons...

This study realised in LISN Laboratory of CEA Saclay, deals with the creep fatigue propagation of semi elliptical crack at the temperature of 650 deg C in 316L(N) stainless steel plates with or without welded joints. A vast majority of the studies on creep fatigue propagation models are based on specimen (CT) especially designed for crack propagation study. The PLAQFLU program performed in LISN laboratory deals with the application and adaptation of these models to complex crack shape, which are more representative of the cracks observed in industrial components. In this scope, we use propagation tests realised at the temperature of 650 deg C with wide plates containing semi elliptical defects. For some of them, the initial defect is machined in the middle of a welded joint, which constitute a privileged site for the crack initiation. The approach used in this study is based on global parameters of fracture mechanics. At first, tests on CT specimen are used in order to determine the propagation laws correlating the crack growth rate to the global parameters K or C * . These laws are then supposed to be intrinsic to our materials and are used to analysed the semi elliptical crack propagation. The analysis of the comportment of the crack during the hold time demonstrates the possibility to establish a correlation between the crack propagation both in the deepest and the surface point and the local value of C * . These correlations are coherent in the different points of the crack front for the different applied hold times, and they present a reasonably good agreement with the creep propagation law identified on CT specimen. The simulation of test performed on based metal specimen with a model of summation of both creep and pure fatigue crack growth gives acceptable results when the calculus of the simplified expression of C * s considers a continuous evolution of creep deformations rate during the all test. (author)

Presently available laser sources can yield powers for which the ponderomotive energy of an electron U p can be equal to or even larger than the rest energy mc 2 of an electron. Therefore it has become of interest to consider fundamental radiation-induced or assisted processes in such powerful laser fields. In the present work we consider laser-induced Compton scattering and laser-assisted electron atom scattering in such fields, assuming that the laser beam has arbitrary ellipticpolarization. We investigate in detail the angular and polarisation dependence of the differential cross-sections of the two laser-induced or laser-assisted nonlinear processes as a function of the order N of absorbed or emitted laser photons ω. The present work is a generalization of our previous analysis of Compton scattering and electron-atom scattering in a linearly polarized laser field. (authors)

The ellipticalpolarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the ellipticalpolarization dependence of β.

We have investigated the properties of TM polarized light in planar photonic crystal waveguide structures, which exhibit photonic band gaps for TE polarized light. Straight and bent photonic crystal waveguides and couplers have been fabricated in silicon-on-insulator material and modelled using a 3......D finite-difference-time-domain method. The simulated spectra are in excellent agreement with the experimental results, which show a propagation loss as low as 2.5±4 dB/mm around 1525 nm and bend losses at 2.9±0.2 dB for TM polarized light. We demonstrate a high coupling for TM polarized light...

We study the pitch attitude dynamics of an asymmetric magnetic spacecraft in a polar almost circular orbit under the influence of a gravity gradient torque. The spacecraft is perturbed by the small eccentricity of the elliptic orbit and by a small magnetic torque generated by the interaction between the Earth's magnetic field and the magnetic moment of the spacecraft. Under both perturbations, we show that the pitch motion exhibits heteroclinic chaotic behavior by means of the Melnikov method. Numerical methods applied to simulations of the pitch motion also confirm the chaotic character of the spacecraft attitude dynamics. Finally, a linear time-delay feedback method for controlling chaos is applied to the governing equations of the spacecraft pitch motion in order to remove the chaotic character of initially irregular attitude motions and transform them into periodic ones.

We study the pitch attitude dynamics of an asymmetric magnetic spacecraft in a polar almost circular orbit under the influence of a gravity gradient torque. The spacecraft is perturbed by the small eccentricity of the elliptic orbit and by a small magnetic torque generated by the interaction between the Earth's magnetic field and the magnetic moment of the spacecraft. Under both perturbations, we show that the pitch motion exhibits heteroclinic chaotic behavior by means of the Melnikov method. Numerical methods applied to simulations of the pitch motion also confirm the chaotic character of the spacecraft attitude dynamics. Finally, a linear time-delay feedback method for controlling chaos is applied to the governing equations of the spacecraft pitch motion in order to remove the chaotic character of initially irregular attitude motions and transform them into periodic ones.

Two-aperture optical and near-infrared polarization and flux measurements of the radio elliptical galaxy IC 5063 are presented. Analysis of the polarized flux shows that the large infrared excess in the nucleus most likely arises from a steep-spectrum non-thermal source with a polarization of 17 per cent and near-infrared luminosity 6x10/sup 41/ erg s/sup -1/. This result suggests that IC5063 is closely related to the more luminous blazars. The origin of the polarization in the optical is, however, not clear.

Two-aperture optical and near-infrared polarization and flux measurements of the radio elliptical galaxy IC 5063 are presented. Analysis of the polarized flux shows that the large infrared excess in the nucleus most likely arises from a steep-spectrum non-thermal source with a polarization of 17 per cent and near-infrared luminosity 6x10 41 erg s -1 . This result suggests that IC5063 is closely related to the more luminous blazars. The origin of the polarization in the optical is, however, not clear. (author)

Polar Mesospheric Clouds (PMCs) are sensitive to changes in temperature of the cold polar summer mesosphere, which in turn are modulated by gravity waves (GWs). In this study we investigate the link between PMCs and GWs that propagate both vertically (i.e. wave propagation is directly above the source region) and obliquely (lateral or non-vertical propagation upward but away from the source region). Several observational studies have analyzed the link between PMCs and vertically propagating GWs and have reported both positive and negative correlations. Moreover, while modelling studies have noted the possibility of oblique propagation of GWs from the low-latitude stratosphere to the high-latitude mesosphere, observational studies of the influence of these waves on the polar summer mesosphere are sparse. We present a comprehensive analysis of the influence of vertically and obliquely propagating GWs on the northern hemisphere (NH) polar summer mesosphere using data from 8 PMC seasons. Temperature data from the SOFIE experiment on the AIM satellite and SABER instrument on the TIMED satellite are used to derive GW parameters. SOFIE PMC data in terms of Ice Water Content (IWC) are used to quantify the changes in the polar summer mesosphere. At high latitudes, preliminary analysis of vertically propagating waves indicate a weak but positive correlation between GWs at 50 km and GWs at the PMC altitude of 84 km. Overall there is a negative correlation between GWs at 50 km and IWC and a positive correlation between GWs at 84 km and IWC. These results and the presence of a slanted structure (slanted from the low-latitude stratosphere to the high-latitude mesosphere) in GW momentum flux suggest the possibility of a significant influence of obliquely propagating GWs on the polar summer mesosphere

We theoretically study laser-scanning confocal fluorescence microscopy using ellipticallypolarized cylindrical vector excitation light as a tool for visualization of arbitrarily oriented single quantum dipole emitters located (1) near planar surfaces enhancing fluorescence, (2) in a thin supported polymer film, (3) in a freestanding polymer film, and (4) in a dielectric planar microcavity. It is shown analytically that by using a tightly focused azimuthally polarized beam, it is possible to exclude completely the orientational dependence of the image intensity maximum of a quantum emitter that absorbs light as a pair of incoherent independent linear dipoles. For linear dipole quantum emitters, the orientational independence degree higher than 0.9 can normally be achieved (this quantity equal to 1 corresponds to completely excluded orientational dependence) if the collection efficiency of the microscope objective and the emitter's total quantum yield are not strongly orientationally dependent. Thus, the visualization of arbitrarily oriented single quantum emitters by means of the studied technique can be performed quite efficiently.

FCC046 is a Fornax Cluster dwarf elliptical galaxy. Optical observations have shown that this galaxy, besides an old and metal-poor stellar population, also contains a very young centrally concentrated population and is actively forming stars, albeit at a very low level. Here, we report on 21 cm observations of FCC046 with the Australia Telescope Compact Array which we conducted in the course of a small survey of Fornax Cluster early-type dwarf galaxies. We have discovered a {approx}10{sup 7} M{sub Sun} H I cloud surrounding FCC046. We show that the presence of this significant gas reservoir offers a concise explanation for this galaxy's optical morphological and kinematical properties. Surprisingly, the H I gas, as evidenced by its morphology and its rotational motion around the galaxy's optical major axis, is kinematically decoupled from the galaxy's stellar body. This is the first time such a ring of gaseous material in minor-axis rotation is discovered around a dwarf galaxy.

Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta J i and J f . The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of J i and J f and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼lξ holds and dichroism occurs only when the photons are ellipticallypolarized, with 0< vertical bar ξ vertical bar <1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons

Control of double ionization of He by means of the polarization and carrier-envelope phase (CEP) of an intense, few-cycle extreme ultraviolet (XUV) pulse is demonstrated numerically by solving the six-dimensional two-electron, time-dependent Schrödinger equation for He interacting with an ellipticallypolarized XUV pulse. Guided by perturbation theory (PT), we predict the existence of a nonlinear dichroic effect (∝I^{3/2}) that is sensitive to the CEP, ellipticity, peak intensity I, and temporal duration of the pulse. This dichroic effect (i.e., the difference of the two-electron angular distributions for opposite helicities of the ionizing XUV pulse) originates from interference of first- and second-order PT amplitudes, allowing one to probe and control S- and D-wave channels of the two-electron continuum. We show that the back-to-back in-plane geometry with unequal energy sharing is an ideal one for observing this dichroic effect that occurs only for an ellipticallypolarized, few-cycle attosecond pulse.

A computational protocol for magneto-chiral dichroism and magneto-chiral birefringence dispersion is presented within the framework of damped response theory, also known as complex polarizationpropagator theory, at the level of time-dependent Hartree–Fock and time-dependent density functional th...

Theoretical and experimental investigations of crack growth under thermal and thermomechanical fatigue loading are presented. The experiments were performed with a ferritic reactor pressure vessel steel 20 MnMoNi 5 5 and an austenitic stainless steel X6 CrNi 18 11. A plate containing a semi-elliptical surface crack is heated up to a homogeneous temperature and cyclically cooled down by a jet of cold water. On the basis of linear elastic fracture mechanics stress-intensity factors are calculated with the weight function method. The prediction of crack growth under thermal fatigue loading using data from mechanical fatigue tests is compared with the experimental result. (orig.) [de

The stimulated Raman backscattering of an intense electromagnetic wave propagating in the extraordinary mode along a uniform, static magnetic field is considered. The dispersion relation for a homogeneous magnetized plasma in the presence of the circularly polarized pump waves is developed in the cold-plasma approximation with the pump frequency above the plasma frequency. Formulas are derived for the threshold νsub(OT) of the parametric instability and for the growth rate γ of the backscattered extraordinary wave and Langmuir wave. The effects of the magnetic field parallel to the direction of propagation on νsub(0T) and γ are studied numerically. (author)

The techniques of propagating spin-wave spectroscopy and current-induced spin-wave Doppler shift are applied to a 20-nm-thick Fe/MgO(001) film. The magnetic parameters extracted from the position of the spin-wave resonance peaks are very close to those tabulated for bulk iron. From the zero-current propagating wave forms, a group velocity of 4 km/s and an attenuation length of about 6 μ m are extracted for 1.6-μ m -wavelength spin wave at 18 GHz. From the measured current-induced spin-wave Doppler shift, we extract a surprisingly high degree of spin polarization of the current of 83 % , which constitutes the main finding of this work. This set of results makes single-crystalline iron a promising candidate for building devices utilizing high-frequency spin waves and spin-polarized currents.

Due to the intimate anisotropic interaction between an XUV light field and a molecule resulting in photoionization (PI), molecular frame photoelectron angular distributions (MFPADs) are most sensitive probes of both electronic/nuclear dynamics and the polarization state of the ionizing light field. Consequently, they encode the complex dipole matrix elements describing the dynamics of the PI transition, as well as the three normalized Stokes parameters s 1 , s 2 , s 3 characterizing the complete polarization state of the light, operating as molecular polarimetry. The remarkable development of advanced light sources delivering attosecond XUV pulses opens the perspective to visualize the primary steps of photochemical dynamics in time-resolved studies, at the natural attosecond to few femtosecond time-scales of electron dynamics and fast nuclear motion. It is thus timely to investigate the feasibility of measurement of MFPADs when PI is induced e.g., by an attosecond pulse train (APT) corresponding to a comb of discrete high-order harmonics. In the work presented here, we report MFPAD studies based on coincident electron-ion 3D momentum imaging in the context of ultrafast molecular dynamics investigated at the PLFA facility (CEA-SLIC), with two perspectives: (i) using APTs generated in atoms/molecules as a source for MFPAD-resolved PI studies, and (ii) taking advantage of molecular polarimetry to perform a complete polarization analysis of the harmonic emission of molecules, a major challenge of high harmonic spectroscopy. Recent results illustrating both aspects are reported for APTs generated in unaligned SF 6 molecules by an ellipticallypolarized infrared driving field. The observed fingerprints of the ellipticallypolarized harmonics include the first direct determination of the complete s 1 , s 2 , s 3 Stokes vector, equivalent to (ψ, ε, P), the orientation and the signed ellipticity of the polarization ellipse, and the degree of polarization P. They are

Analyzing the connectome of a nervous system provides valuable information about the functions of its subsystems. Although much has been learned about the architectures of neural networks in various organisms by applying analytical tools developed for general networks, two distinct and functionally important properties of neural networks are often overlooked. First, neural networks are endowed with polarity at the circuit level: Information enters a neural network at input neurons, propagates through interneurons, and leaves via output neurons. Second, many functions of nervous systems are implemented by signal propagation through high-level pathways involving multiple and often recurrent connections rather than by the shortest paths between nodes. In the present study, we analyzed two neural networks: the somatic nervous system of Caenorhabditis elegans (C. elegans) and the partial central complex network of Drosophila, in light of these properties. Specifically, we quantified high-level propagation in the vertical and horizontal directions: the former characterizes how signals propagate from specific input nodes to specific output nodes and the latter characterizes how a signal from a specific input node is shared by all output nodes. We found that the two neural networks are characterized by very efficient vertical and horizontal propagation. In comparison, classic small-world networks show a trade-off between vertical and horizontal propagation; increasing the rewiring probability improves the efficiency of horizontal propagation but worsens the efficiency of vertical propagation. Our result provides insights into how the complex functions of natural neural networks may arise from a design that allows them to efficiently transform and combine input signals.

Context. Polar corona is often explored to find the energy source for the acceleration of the fast solar wind. Earlier observations show omni-presence of quasi-periodic disturbances, traveling outward, which is believed to be caused by the ubiquitous presence of outward propagating waves. These waves, mostly of compressional type, might provide the additional momentum and heat required for the fast solar wind acceleration. It has been conjectured that these disturbances are not due to waves but high speed plasma outflows, which are difficult to distinguish using the current available techniques. Aims: With the unprecedented high spatial and temporal resolution of AIA/SDO, we search for these quasi-periodic disturbances in both plume and interplume regions of the polar corona. We investigate their nature of propagation and search for a plausible interpretation. We also aim to study their multi-thermal nature by using three different coronal passbands of AIA. Methods: We chose several clean plume and interplume structures and studied the time evolution of specific channels by making artificial slits along them. Taking the average across the slits, space-time maps are constructed and then filtration techniques are applied to amplify the low-amplitude oscillations. To suppress the effect of fainter jets, we chose wider slits than usual. Results: In almost all the locations chosen, in both plume and interplume regions we find the presence of propagating quasi-periodic disturbances, of periodicities ranging from 10-30 min. These are clearly seen in two channels and in a few cases out to very large distances (≈250″) off-limb, almost to the edge of the AIA field of view. The propagation speeds are in the range of 100-170 km s-1. The average speeds are different for different passbands and higher in interplume regions. Conclusions: Propagating disturbances are observed, even after removing the effects of jets and are insensitive to changes in slit width. This indicates

We present a new implementation of the second-order polarizationpropagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear...... and triplet transitions for benzene and naphthalene. The results compare well with experiment and CASPT2 values, calculated with identical basis sets and molecular geometries. This indicates that SOPPA can provide reliable values for excitation energies and response properties for relatively large molecular...

The influence of polarization on millimeter wave propagation is investigated from both an experimental and a theoretical viewpoint. First, previous theoretical and experimental work relating to the attenuation and depolarization of millimeter waves by rainfall is discussed. Considerable detail is included in the literature review. Next, a theoretical model is developed to predict the cross polarization level during rainfall from the path average rain rate and the scattered field from a single raindrop. Finally, data from the VPI and SU depolarization experiment are presented as verification of the new model, and a comparison is made with other theories and experiments. Aspects of the new model are: (1) spherical rather than plane waves are assumed, (2) the average drop diameter is used rather than a drop size distribution, and (3) it is simple enough so that the effect which changing one or more parameters has on the crosspolarization level is easily seen.

Full Text Available The presence of (first and second orders polarization mode dispersion (PMD, chromatic dispersion, and initial chirp makes effects on the propagated pulses in single mode fiber. Nowadays, there is not an accurate mathematical formula that describes the pulse shape in the presence of these effects. In this work, a theoretical study is introduced to derive a generalized formula. This formula is exactly approached to mathematical relations used in their special cases. The presence of second-order PMD (SOPMD will not affect the orthogonality property between the principal states of polarization. The simulation results explain that the interaction of the SOPMD components with the conventional effects (chromatic dispersion and chirp will cause a broadening/narrowing and shape distortion. This changes depend on the specified values of SOPMD components as well as the present conventional parameters.

In recent years, the use of shielding gas to prevent the diffusion of the ambient air, particularly oxygen and nitrogen species, into the effluent of the atmospheric pressure plasma jet, and thus control the nature of chemical species used in the plasma treatment has increased. In this paper, the radial propagation of a plasma jet in ambient Ar is examined to find the key determinants of the polarity of plasma jets. The dynamics of the discharge reveal that the radial diffusion discharge is a special phenomenon observed only at the falling edge of the pulses. The radial transport of electrons, which is driven by the radial component of the applied electric field at the falling edge of the pulse, is shown to play an important role in increasing the seed electron density in the surrounding Ar. This result suggests a method to provide seed electrons at atmospheric pressure with a negative discharge. The polarity of the plasma jet is found to be determined by the pulse width rather than the polarity of the applied voltage, as it dictates the relative difference in the intensity of the two discharges in a single pulse, where the stronger discharge in a pulse dominates the behavior of the plasma jet. Accordingly, a method to control the polarity of a plasma jet through varying the pulse width is developed. Since plasma jets of different polarities differ remarkably in terms of their characteristics, the method to control the polarity reported in this paper will be of use for such applications as plasma-enhanced processing of materials and plasma biomedicine.

In recent years, the use of shielding gas to prevent the diffusion of the ambient air, particularly oxygen and nitrogen species, into the effluent of the atmospheric pressure plasma jet, and thus control the nature of chemical species used in the plasma treatment has increased. In this paper, the radial propagation of a plasma jet in ambient Ar is examined to find the key determinants of the polarity of plasma jets. The dynamics of the discharge reveal that the radial diffusion discharge is a special phenomenon observed only at the falling edge of the pulses. The radial transport of electrons, which is driven by the radial component of the applied electric field at the falling edge of the pulse, is shown to play an important role in increasing the seed electron density in the surrounding Ar. This result suggests a method to provide seed electrons at atmospheric pressure with a negative discharge. The polarity of the plasma jet is found to be determined by the pulse width rather than the polarity of the applied voltage, as it dictates the relative difference in the intensity of the two discharges in a single pulse, where the stronger discharge in a pulse dominates the behavior of the plasma jet. Accordingly, a method to control the polarity of a plasma jet through varying the pulse width is developed. Since plasma jets of different polarities differ remarkably in terms of their characteristics, the method to control the polarity reported in this paper will be of use for such applications as plasma-enhanced processing of materials and plasma biomedicine.

Full Text Available We conduct a statistical analysis of the coherence and phase difference of low frequency geomagnetic fluctuations between two Antarctic stations, Mario Zucchelli Station (geographic coordinates: 74.7° S, 164.1° E; corrected geomagnetic coordinates: 80.0° S, 307.7° E and Scott Base (geographic coordinates: 77.8° S 166.8° E; corrected geomagnetic coordinates: 80.0° S 326.5° E, both located in the polar cap. Due to the relative position of the stations, whose displacement is essentially along a geomagnetic parallel, the phase difference analysis allows to determine the direction of azimuthal propagation of geomagnetic fluctuations. The results show that coherent fluctuations are essentially detectable around local geomagnetic midnight and, in a minor extent, around noon; moreover, the phase difference reverses in the night time hours, indicating a propagation direction away from midnight, and also around local geomagnetic noon, indicating a propagation direction away from the subsolar point. The nigh time phase reversal is more clear for southward interplanetary magnetic field conditions, suggesting a relation with substorm activity.

The introduction, in this analysis, of the Interplanetary Magnetic Field conditions, gave interesting results, indicating a relation with substorm activity during nighttime hours.

We also conducted a study of three individual pulsation events in order to find a correspondence with the statistical behaviour. In particular, a peculiar event, characterized by quiet magnetospheric and northward interplanetary magnetic field conditions, shows a clear example of waves propagating away from the local geomagnetic noon; two more events, occurring during southward interplanetary magnetic field conditions, in one case even during a moderate storm, show waves propagating away from the local geomagnetic midnight.

Full Text Available We conduct a statistical analysis of the coherence and phase difference of low frequency geomagnetic fluctuations between two Antarctic stations, Mario Zucchelli Station (geographic coordinates: 74.7° S, 164.1° E; corrected geomagnetic coordinates: 80.0° S, 307.7° E and Scott Base (geographic coordinates: 77.8° S 166.8° E; corrected geomagnetic coordinates: 80.0° S 326.5° E, both located in the polar cap. Due to the relative position of the stations, whose displacement is essentially along a geomagnetic parallel, the phase difference analysis allows to determine the direction of azimuthal propagation of geomagnetic fluctuations. The results show that coherent fluctuations are essentially detectable around local geomagnetic midnight and, in a minor extent, around noon; moreover, the phase difference reverses in the night time hours, indicating a propagation direction away from midnight, and also around local geomagnetic noon, indicating a propagation direction away from the subsolar point. The nigh time phase reversal is more clear for southward interplanetary magnetic field conditions, suggesting a relation with substorm activity. The introduction, in this analysis, of the Interplanetary Magnetic Field conditions, gave interesting results, indicating a relation with substorm activity during nighttime hours. We also conducted a study of three individual pulsation events in order to find a correspondence with the statistical behaviour. In particular, a peculiar event, characterized by quiet magnetospheric and northward interplanetary magnetic field conditions, shows a clear example of waves propagating away from the local geomagnetic noon; two more events, occurring during southward interplanetary magnetic field conditions, in one case even during a moderate storm, show waves propagating away from the local geomagnetic midnight.

Helium double photoionization (γ,2e) triple differential cross sections (TDCSs) were measured at an excess energy of 60 eV using a dual toroidal spectrometer and synchrotron radiation from a helical undulator (BL-28A, Photon Factory, Japan). Energy-sharing ratios (R=E 2 /E 1 ) for the two ejected electrons of 5 and 11 are studied with both right- and left-handed ellipticallypolarized light. The TDCSs are found to be in good agreement with those obtained using the hyperspherical R matrix with semiclassical outgoing waves theory. The circular dichroism for a limited mutual angular range (φ 12 ≅110 deg. -200 deg.) is determined from the experimental data for both R=5 and 11, and compared to theoretical calculations performed over the complete range of mutual angles. No dynamic nodes are found in either the experimental (within the explored φ 12 range) or theoretical circular dichroism for these R values at this excess energy

It has recently been suggested that two counter-propagating, circularly polarized, ultra-intense lasers can induce a strong electron spin polarization at the magnetic node of the electromagnetic field that they setup (Del Sorbo et al 2017 Phys. Rev. A 96 043407). We confirm these results by considering a more sophisticated description that integrates over realistic trajectories. The electron dynamics is weakly affected by the variation of power radiated due to the spin polarization. The degree of spin polarization differs by approximately 5% if considering electrons initially at rest or already in a circular orbit. The instability of trajectories at the magnetic node induces a spin precession associated with the electron migration that establishes an upper temporal limit to the polarization of the electron population of about one laser period.

The known analytic expressions for the evolution of the polarization of electromagnetic waves propagating in a plasma with uniformly sheared magnetic field are extended to the case where the shear is not constant. Exact analytic expressions are found for the case when the space variations of the medium are such that the magnetic field components and the plasma density satisfy a particular condition (eq. 13), possibly in a convenient reference frame of polarization space [it

This study realised in LISN Laboratory of CEA Saclay, deals with the creep fatigue propagation of semi elliptical crack at the temperature of 650 deg C in 316L(N) stainless steel plates with or without welded joints. A vast majority of the studies on creep fatigue propagation models are based on specimen (CT) especially designed for crack propagation study. The PLAQFLU program performed in LISN laboratory deals with the application and adaptation of these models to complex crack shape, which are more representative of the cracks observed in industrial components. In this scope, we use propagation tests realised at the temperature of 650 deg C with wide plates containing semi elliptical defects. For some of them, the initial defect is machined in the middle of a welded joint, which constitute a privileged site for the crack initiation. The approach used in this study is based on global parameters of fracture mechanics. At first, tests on CT specimen are used in order to determine the propagation laws correlating the crack growth rate to the global parameters K or C{sup *}. These laws are then supposed to be intrinsic to our materials and are used to analysed the semi elliptical crack propagation. The analysis of the comportment of the crack during the hold time demonstrates the possibility to establish a correlation between the crack propagation both in the deepest and the surface point and the local value of C{sup *}. These correlations are coherent in the different points of the crack front for the different applied hold times, and they present a reasonably good agreement with the creep propagation law identified on CT specimen. The simulation of test performed on based metal specimen with a model of summation of both creep and pure fatigue crack growth gives acceptable results when the calculus of the simplified expression of C{sup *}{sub s} considers a continuous evolution of creep deformations rate during the all test. (author)

Tamm plasmons are confined optical states at the interface of a metal and a dielectric Bragg mirror. Unlike conventional surface plasmons, Tamm plasmons may be directly excited by an external light source in both TE and TM polarizations. Here we consider the one-dimensional propagation of Tamm plasmons under long and narrow metallic stripes deposited on top of a semiconductor Bragg mirror. The spatial confinement of the field imposed by the stripe and its impact on the structure and energy of Tamm modes are investigated. We show that the Tamm modes are coupled to surface plasmons arising at the stripe edges. These plasmons form an interference pattern close to the bottom surface of the stripe that involves modification of both the energy and loss rate for the Tamm mode. This phenomenon is pronounced only in the case of TE polarization of the Tamm mode. These findings pave the way to application of laterally confined Tamm plasmons in optical integrated circuits as well as to engineering potential traps for both Tamm modes and hybrid modes of Tamm plasmons and exciton polaritons with meV depth.

The global array of High Frequency (HF) Super Dual Auroral Radar Network (SuperDARN) radars continuously monitors ionospheric convection in the middle-to-high latitude region. The radars measure coherent backscatter from decameter scale field-aligned irregularities. One of the main generation mechanisms for these field-aligned irregularities is the gradient drift instability (GDI). The edges of ionospheric density structures, such as polar cap patches, provide ideal locations for GDI growth. The geometry required for GDI growth results in irregularities forming on the trailing edge of polar patches. However, irregularities generated by the non-linear evolution of the GDI can become prevalent throughout the patch within minutes. Modelling the irregularity growth and measurements of backscatter within patches have both confirmed this. One aspect that has often been overlooked in studies of coherent backscatter within patches is the effect of HF propagation on echo location. This study examines HF echo locations in the vicinity of patches that were imaged using the Resolute Bay Incoherent Scatter Radars (RISR). The effect of both vertical and lateral refraction of the HF wave on echo location is examined.

A dispersive full-wave finite-difference time-domain (FDTD) model is used to calculate the performance of elliptic cylindrical cloaking devices. The permittivity and the permeability tensors for the cloaking structure are derived by using an effective medium approach in general relativity. The elliptic cylindrical invisibility devices are found to show imperfect cloaking, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of the propagation of those waves, the semi-focal distances and the loss tangents of the meta-material. When the semifocal distance of the elliptic cylinder decreases, the performance of the cloaking becomes very good, with neither noticeable scatterings nor field penetrations. For a larger semi-focal distance, only the TM wave with a specific propagation direction shows good cloaking performance. Realistic cloaking materials with loss still show a cloak that is working, but attenuated back-scattering waves exist.

A high birefringence and ultra-high nonlinearity photonic crystal fiber (PCF) is proposed, which is composed of an elliptical As2Se3-doped core and an inner cladding with hexagonal lattice. Optical properties of the PCF are simulated by the full-vector finite element method. The simulation results show that the high birefringence of ∼0.33, ultra-high-nonlinearity coefficient of 300757 W-1km-1 and the low confinement loss can be achieved in the proposed PCF simultaneously at the wavelength of 1.55 μm. Furthermore, by comparison with the other two materials (80PbO•20Ga2O3, As2S3) filled in the core, the As2Se3-doped PCF is found to have the highest birefringence and nonlinearity due to its higher refractive index and nonlinear refractive index. The flattened dispersion feature, as well as the low confinement loss of the proposed PCF structure make it suitable as a wide range of applications, such as the coherent optical communications, polarization-maintaining and nonlinear optics, etc.

The polarization characteristics of an artificial laser source in space were measured through space-to-ground atmospheric transmission paths. An existing Japanese laser communication satellite and optical ground station were used to measure Stokes parameters and the degree of polarization of the laser beam transmitted from the satellite. As a result, the polarization was preserved within an rms error of 1.6 degrees, and the degree of polarization was 99.4+/-4.4% through the space-to-ground atmosphere. These results contribute to the link estimation for quantum key distribution via space and provide the potential for enhancements in quantum cryptography worldwide in the future.

Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

Full Text Available This work presents fast and simple method for evaluation of polarization correction to scalar propagation constant of arbitrary order guided modes propagating over weakly guiding optical fibers. Proposed solution is based on earlier on developed modified Gaussian approximation extended for analysis of weakly guiding optical fibers with arbitrary refractive index profile in the core region bounded by single solid outer cladding. Some results are presented that illustrate the decreasing of computational error during the estimation of propagation constant when polarization corrections are taken into account. Analytical expressions for the first and second derivatives of polarization correction are derived and presented.

We report on the theory and experimental generation of a class of diffraction-attenuation-resistant beams with state of polarization (SOP) and intensity that can be controlled on demand along the propagation direction. This control is achieved by a suitable superposition of Bessel beams, whose parameters are systematically chosen based on closed-form analytic expressions provided by the frozen waves method. Using an amplitude-only spatial light modulator, we experimentally demonstrate three scenarios. In the first, the SOP of a horizontally polarized beam evolves to radial polarization and is then changed to vertical polarization, with the beam intensity held constant. In the second, we simultaneously control the SOP and the longitudinal intensity profile, which is chosen such that the beam's central ring can be switched off over predefined space regions, thus generating multiple foci with different SOPs and at different intensity levels along the propagation. Finally, the ability to control the SOP while overcoming attenuation inside lossy fluids is shown experimentally. We envision our proposed method to be of great interest for many applications, such as optical tweezers, atom guiding, material processing, microscopy, and optical communications.

Based on the idea of coordinate transformation (Pendry, Schurig and Smith 2006 Science 312 1780), arbitrarily elliptical-cylindrical cloaks are proposed and designed. The elliptical cloak, which is composed of inhomogeneous anisotropic metamaterials in an elliptical-shell region, will deflect incoming electromagnetic (EM) waves and guide them to propagate around the inner elliptical region. Such EM waves will return to their original propagation directions without distorting the waves outside the elliptical cloak. General formulations of the inhomogeneous and anisotropic permittivity and permeability tensors are derived for arbitrarily elliptical axis ratio k, which can also be used for the circular cloak when k = 1. Hence the elliptical cloaks can make a large range of objects invisible, from round objects (when k approaches 1) to long and thin objects (when k is either very large or very small). We also show that the material parameters in elliptical cloaking are singular at only two points, instead of on the whole inner circle for circular cloaking, which are much easier to be realized in actual applications. Full-wave simulations are given to validate the arbitrarily elliptical cloaking

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

The nonlinear polarization effects in a birefringent single mode optical fiber is studied using Jacobi elliptic functions. We find that the polarization state of the propagating beam depends on the initial polarization as well as the intensity of the input light in a complicated way. The Stokes polarization parameters are either periodic or aperiodic depending on the value of the Jacobian modulus. Our calculations suggest that the effective beat length of the fiber can become infinite at a higher critical value of the input power when polarization dependent losses are considered. (author)

Full Text Available We present here an experimental demonstration of the wavelength dependence of the polarization singularities due to linear combination of the vector modes excited directly in a two-mode optical fiber. The coherent superposition of the vector modes excited by linearly polarized Gaussian beam as offset skew rays propagated in a helical path inside the fiber results in the generation of phase singular beams with edge dislocation in the fiber output. The polarization character of these beams is found to change dramatically with wavelength—from left-handed ellipticallypolarized edge dislocation to right-handed ellipticallypolarized edge-dislocation through disclinations. The measured behaviour is understood as being due to intermodal dispersion of the polarization corrections to the propagating vector modes, as the wavelength of the input beam is scanned.

We study the paraxial propagation of the radially polarized Airy beams (RPAiBs) in uniaxial crystals orthogonal to the optical axis analytically and numerically. The propagation trajectory, the intensity and the radiation forces of the RPAiBs are investigated and the properties are elucidated by numerical examples in this paper. Results show that the RPAiBs evolve into the beams produced by the x-direction electric field (RPAiXBs) and the y-direction electric field (PRAiYBs) which are totally different in uniaxial crystals. During the propagation, the intensity of the RPAiXBs transfers from the side lobe in the x-direction to the main lobe and finally returns to the side lobe in the x-direction again, but that of the RPAiYBs transfers from the side lobe in the y-direction to the main lobe and flows to the side lobe in the x-direction at last. The effect of the intensity focusing for the RPAiXBs can be modulated by the ratio of the extraordinary index (ne) to the ordinary index (no) in anisotropic medium, which contributes to the intensity focusing of the RPAiBs in a short distance a lot. We can adjust the intensity distribution especially the focusing position, the propagation trajectory and the radiation forces distributions of the RPAiXBs through choosing an appropriate value of the ratio of ne to no to meet the actual usage accordingly.

Full Text Available The authors investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. They outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial...

A combined experimental and theoretical study on mechanistic aspects of polymerization of conjugated polar alkenes by frustrated Lewis pairs (FLPs) based on N-heterocyclic carbene (NHC) and Al(C6F5)3 pairs is reported. This study consists of three key parts: structural characterization of active propagating intermediates, propagation kinetics, and chain-termination pathways. Zwitterionic intermediates that simulate the active propagating species in such polymerization have been generated or isolated from the FLP activation of monomers such as 2-vinylpyridine and 2-isopropenyl-2-oxazoline-one of which, IMes+-CH2C(Me)=(C3H2NO)Al(C6F5)3 - (2), has been structurally characterized. Kinetics performed on the polymerization of 2-vinylpyridine by ItBu/Al(C6F5)3 revealed that the polymerization follows a zero-order dependence on monomer concentration and a first-order dependence on initiator (ItBu) and activator [Al(C6F5)3] concentrations, indicating a bimolecular, activated monomer propagation mechanism. The Lewis pair polymerization of conjugate polar alkenes such as methacrylates is accompanied by competing chain-termination side reactions; between the two possible chain-termination pathways, the one that proceeds via intramolecular backbiting cyclization involving nucleophilic attack of the activated ester group of the growing polymer chain by the O-ester enolate active chain end to generate a six-membered lactone (δ-valerolactone)-terminated polymer chain is kinetically favored, but thermodynamically disfavored, over the pathway leading to the -ketoester-terminated chain, as revealed by computational studies.

We present a formulation of the polarizable density embedding (PDE) method in combination with the complex polarizationpropagator (CPP) method for the calculation of absorption spectra of molecules in solutions. The method is particularly useful for the calculation of near-edge X-ray absorption...... fine structure (NEXAFS) spectra. We compare the performance of PDE-CPP with the previously formulated polarizable embedding (PE)-CPP model for the calculation of the NEXAFS spectra of adenine, formamide, glycine, and adenosine triphosphate (ATP) in water at the carbon and nitrogen K-edges, as well...

The polarization plane of the cosmic microwave background radiation (CMBR) can be rotated either in a space-time with metric of anisotropic type and in a magnetized plasma or in the presence of a quintessential background with pseudoscalar coupling to electromagnetism. A unified treatment of these three phenomena is presented for cold anisotropic plasma at the pre-recombination epoch. It is argued that the generalized expressions derived in the present study may be relevant for direct searches of a possible rotation of the cosmic microwave background polarization.

A beam of fully polarized cold neutrons was transported through a zero magnetic field region of 70 m length without loss of polarization. The purpose of this exercise was twofold: Firstly, to demonstrate that the new zero-field neutron spin-echo method will work also for very long neutron flight paths; secondly, to prove in the most direct way that the neutron free-flight region of the ILL neutron-antineutron oscillation experiment was indeed sufficiently field-free ('quasifree condition') by using the neutrons themselves as a magnetometer. To this purpose the residual magnetic field integrals in the long 'zero-field' region were measured with a conventional neutron spin-echo method. The overall spin precession angle of the neutrons during their flight through the long zero-field region was found to be less than 2 0 . (orig.)

We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between -21 and -22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.

2) wave function coupled to PCM, we introduce dynamical PCM solvent effects only in the Random Phase Approximation (RPA) part of the SOPPA response equations while the static solvent contribution is kept in both the RPA terms as well as in the higher order correlation matrix components of the SOPPA...... response equations. By dynamic terms, we refer to contributions that describe a change in environmental polarization which, in turn, reflects a change in the core molecular charge distribution upon an electronic excitation. This new combination of methods is termed PCM-SOPPA/RPA. We apply this newly...... defined method to the challenging cases of solvent effects on the lowest and intense electronic transitions in o-, m- and p-nitroaniline and o-, m- and p-nitrophenol and compare the performance of PCM-SOPPA/RPA with more conventional approaches. Compared to calculations based on time-dependent density...

We provide a simple theoretical study of beams non-uniformly polarized across their transverse sections which can be introduced in undergraduate optics courses. In order to generate such beams we propose to use a slightly convergent (or divergent) linearly and uniformly polarized beam impinging on an anisotropic uniaxial material with the beam propagation direction along the optic axis. Analytical expressions for the Jones vector, Stokes parameters, ellipticity and azimuth at each point of the transverse section, perpendicular to the propagation direction, are obtained at the output of this system. By means of these parameters a detailed description of the state of polarization across the transverse profile is given

key parts: structural characterization of active propagating intermediates, propagation kinetics, and chain-termination pathways. Zwitterionic intermediates that simulate the active propagating species in such polymerization have been generated

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively. (paper)

An intensity-dependent change in the ellipticity of an input light beam leads to a characteristic shift in polarization instability. Dichroism gives rise to a self-induced ellipticity effect in the polarization state of an intense input light oriented along the fast axis of a birefringent optical fiber. The critical power at which the fiber effective beat length becomes infinite is reduced considerably in the presence of dichroism. (author)

We study the ellipticity dependence of the near-threshold (NT) harmonics of pre-aligned H2 molecules using the time-dependent density functional theory. The anomalous maximum appearing at a non-zero ellipticity for the generated NT harmonics can be attributed to multiphoton effects of the orthogonally polarized component of the elliptical driving laser field. Our calculation also shows that the structure of the bound-state, such as molecular alignment and bond length, can be sensitively reflected on the ellipticity dependence of the near-threshold harmonics.

The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for areapreserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.

Vertically propagating low-frequency inertia-gravity waves (IGWs) are retrieved from meteor radar winds observed at King Sejong Station (KSS: 62.22°S, 58.78°W), Antarctica. IGW horizontal winds extracted from temporal band-pass filtering in regular time-height bins show the frequent occurrence of IGWs with the downward phase progression and the counterclockwise rotation of their horizontal wind vectors with time (i.e., upward energy propagation) near the mesopause region throughout the whole year of 2014. The vertical wavelengths of the observed IGWs roughly range from 14 km to more than 20 km, which is consistent with previous observational studies on the mesospheric IGWs over Antarctica. Stokes parameters and rotary spectra computed from the hodographs of the IGW horizontal wind components reveal that the intrinsic frequencies of the upward propagating IGWs are |f|-3|f| with seasonal variations of the relative predominance between |f|-2|f| and 2|f|-3|f|, where f is the Coriolis parameter at KSS. The hodograph analysis also indicates that the N-S propagation is dominant in austral summer, while the NE-SW propagation is pronounced in austral winter. The propagation direction is discussed in relation to the generation of IGWs due to dynamical imbalances occurring in the tropospheric and stratospheric jet flow systems. Ray tracing results indicate that the N-S propagation in summer may be due to the jet flow systems roughly north of KSS and the NE-SW propagation in winter may be either the SW propagation from the jet flow systems northeast of KSS or the NE propagation (around the South Pole) from the south of Australia and Southern Indian and Pacific Oceans.

A general technique is developed for the analysis of proposed experimental studies of possible P,T-violating effects in the neutron-nucleus interaction based on low-energy neutron transmission through polarized matter. The analysis is applied to proposed experimental schemes and we determine the levels at which the absolute neutron polarization, magnetic fields, and target polarization must be controlled in order for these experiments to obtain a given sensitivity to P,T-violating effects

We experimentally address the wave-vector and polarization dependence of the internal conical refraction phenomenon by demonstrating that an input light beam of elliptical transverse profile refracts into two beams after passing along one of the optic axes of a biaxial crystal, i.e. it exhibits double refraction instead of refracting conically. Such double refraction is investigated by the independent rotation of a linear polarizer and a cylindrical lens. Expressions to describe the position and the intensity pattern of the refracted beams are presented and applied to predict the intensity pattern for an axicon beam propagating along the optic axis of a biaxial crystal.

In this research, based on an analytical expression for cross-spectral density (CSD) matrix elements, coherence and polarization properties of phase-locked partially coherent flat-topped (PCFT) radial array laser beams propagating through weak oceanic turbulence are analyzed. Spectral degrees of coherence and polarization are analytically calculated using CSD matrix elements. Also, the effective width of spatial degree of coherence (EWSDC) is calculated numerically. The simulation is done by considering the effects of source parameters (such as radius of the array setup's circle, effective width of the spectral degree of coherence, and wavelength) and turbulent ocean factors (such as the rate of dissipation of the turbulent kinetic energy per unit mass of fluid and relative strength of temperature and salinity fluctuations, Kolmogorov micro-scale, and rate of dissipation of the mean squared temperature) in detail. Results indicate that any change in the amount of turbulence factors that increase the turbulence power reduces the EWSDC significantly and causes the reduction in the degree of polarization, and occurs at shorter propagation distances but with smaller magnitudes. In addition, being valid for all conditions, the degradation rate of the EWSDC of Gaussian array beams are more in comparison with the PCFT ones. The simulation and calculation results are shown by graphs.

A time-domain analysis of the propagation properties of surface-plasmon-polaritons (SPP) in Silver nanostructures is presented. The analysis is based on a simulation algorithm that unifies the formulation of different dispersion models and multi-pole relations into one form. The main objective of this work is to perform a comparative analysis between different dispersion models used for Silver, including Debye, Drude and multi-pole Lorentz-Drude models. The quantities that are used in the comparison are the SPP propagation length and propagation speed. Experimental results reported in literature are used to support the conclusions.

A time-domain analysis of the propagation properties of surface-plasmon-polaritons (SPP) in Silver nanostructures is presented. The analysis is based on a simulation algorithm that unifies the formulation of different dispersion models and multi

The nonlinear dynamics of a circularly polarized laser pulse propagating in the magnetized plasmas whose constituents are superthermal ions and mixed nonthermal high-energy tail electrons is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude is obtained using a relativistic two-fluid model. Based on this nonlinear equation and taking into account some nonlinear phenomena such as modulational instability, self-focusing and soliton formation are investigated. Effect of the magnetized plasma with superthermal ions and mixed nonthermal high-energy tail electrons on these phenomena is considered. It is shown that the nonthermality and superthermality of particles can substantially change the nonlinearity of medium.

The nonlinear dynamics of a circularly polarized laser pulse propagating in the magnetized plasmas whose constituents are superthermal ions and mixed nonthermal high-energy tail electrons is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude is obtained using a relativistic two-fluid model. Based on this nonlinear equation and taking into account some nonlinear phenomena such as modulational instability, self-focusing and soliton formation are investigated. Effect of the magnetized plasma with superthermal ions and mixed nonthermal high-energy tail electrons on these phenomena is considered. It is shown that the nonthermality and superthermality of particles can substantially change the nonlinearity of medium.

We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families {A}_{N-1}, {B}_N, {C}_N and {D}_N, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.

I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera — explicitly verifying this in the cases of the quintic in ℙ{sup 4}, the sextic in Wℙ{sub (2,1,1,1,1)}, the octic in Wℙ{sub (4,1,1,1,1)} and the dectic in Wℙ{sub (5,2,1,1,1)}. With an input of the corresponding ‘single-center’ indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in N=2 supergravity.

We study the ellipticity of near-threshold harmonics (NTH) from aligned molecules with large internuclear distances numerically and analytically. The calculated harmonic spectra show a broad plateau for NTH which is several orders of magnitude higher than that for high-order harmonics. In particular, the NTH plateau shows high ellipticity at small and intermediate orientation angles. Our analyses reveal that the main contributions to the NTH plateau come from the transition of the electron from continuum states to these two lowest bound states of the system, which are strongly coupled together by the laser field. Besides continuum states, higher excited states also play a role in the NTH plateau, resulting in a large phase difference between parallel and perpendicular harmonics and accordingly high ellipticity of the NTH plateau. The NTH plateau with high intensity and large ellipticity provides a promising manner for generating strong elliptically-polarized extreme-ultraviolet (EUV) pulses.

The existence of a triaxial shape for elliptical galaxies has been considered in recent years to explain the new kinematical and geometrical findings, i.e. (a) the low rotation/velocity dispersion ratio found also in some flat systems, (b) the presence of twisting in the isophotes, (c) the recently found correlation between maximum twisting and maximum flattening, (d) the presence of rotation along the minor axis. A simple geometrical model of elliptical galaxies having shells with different axial ratios c/a, b/a has been produced to interpret three fundamental key-features of elliptical galaxies: (i) the distribution of the maximum flattening observed; (ii) the percentage of ellipticals showing twisting; and (iii) the correlation between maximum twisting and maximum flattening. The model has been compared with observational data for 348 elliptical systems as given by Strom and Strom. It is found that a triaxial ellipsoid with coaxial shells having axial ratios c/a and b/a mutually dependent in a linear way can satisfy the observations.

Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.

Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.

We give a brief overview of the history, state of the art, and future for elliptical superconducting cavities. Principles of the cell shape optimization, criteria for multi-cell structures design, HOM damping schemes and other features are discussed along with examples of superconducting structures for various applications.

For the calculation of adiabatic singlet-triplet gaps (STG) in diradicaloid systems the spin-flip (SF) variant of the algebraic diagrammatic construction (ADC) scheme for the polarizationpropagator in third order perturbation theory (SF-ADC(3)) has been applied. Due to the methodology of the SF approach the singlet and triplet states are treated on an equal footing since they are part of the same determinant subspace. This leads to a systematically more accurate description of, e.g., diradicaloid systems than with the corresponding non-SF single-reference methods. Furthermore, using analytical excited state gradients at ADC(3) level, geometry optimizations of the singlet and triplet states were performed leading to a fully consistent description of the systems, leading to only small errors in the calculated STGs ranging between 0.6 and 2.4 kcal/mol with respect to experimental references.

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

During 1999 August 18, both Cassini and WIND were in the Earth's magnetosheath and detected transverse electromagnetic waves instead of the more typical mirror-mode emissions. The Cassini wave amplitudes were as large as ∼14 nT (peak to peak) in a ∼55 nT ambient magnetic field B {sub 0}. A new method of analysis is applied to study these waves. The general wave characteristics found were as follows. They were left-hand polarized and had frequencies in the spacecraft frame (f {sub scf}) below the proton cyclotron frequency (f{sub p} ). Waves that were either right-hand polarized or had f {sub scf} > f{sub p} are shown to be consistent with Doppler-shifted left-hand waves with frequencies in the plasma frame f{sub pf} < f{sub p} . Thus, almost all waves studied are consistent with their being electromagnetic proton cyclotron waves. Most of the waves (∼55%) were found to be propagating along B {sub 0} (θ{sub kB{sub 0}}<30{sup ∘}), as expected from theory. However, a significant fraction of the waves were found to be propagating oblique to B {sub 0}. These waves were also circularly polarized. This feature and the compressive ([B {sub max} – B {sub min}]/B {sub max}, where B {sub max} and B {sub min} are the maximum and minimum field magnitudes) nature (ranging from 0.27 to 1.0) of the waves are noted but not well understood at this time. The proton cyclotron waves were shown to be quasi-coherent, theoretically allowing for rapid pitch-angle transport of resonant protons. Because Cassini traversed the entire subsolar magnetosheath and WIND was in the dusk-side flank of the magnetosheath, it is surmised that the entire region was filled with these waves. In agreement with past theory, it was the exceptionally low plasma β (0.35) that led to the dominance of the proton cyclotron wave generation during this interval. A high-speed solar wind stream ((V{sub sw} ) = 598 km s{sup –1}) was the source of this low-β plasma.

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity ε and permeability μ are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide

The dispersion relations of two-dimensional photonic crystals made of uniaxial polaritonic cylinders arranged in triangular lattice are calculated. The particular case of the transverse magnetic polarization is taken into account. Three different uniaxial materials showing transverse phonon-polariton excitations are considered: aluminum nitride, gallium nitride, and indium nitride. The study is carried out by means of the finite-difference time-domain technique for the solution of Maxwell equations, together with the method of the auxiliary differential equation. It is shown that changing the filling fraction can result in the modification of both the photonic and polaritonic bandgaps in the optical dispersion relations. Wider gaps appear for smaller filling fraction values, whereas a larger number of photonic bandgaps will occur within the frequency range considered when a larger filling fraction is used. The effect of including the distinct wurtzite III-V nitride semiconductors as core materials in the cylinders embedded in the air on the photonic properties is discussed as well, highlighting the effect of the dielectric anisotropy on the properties of the polaritonic part of the photonic spectrum.

A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

Radiation from magnetized plasmas is in general ellipticallypolarized. In order to convert the ellipticalpolarization to linear polarization, mirrors with grooved surfaces are currently employed in our collective Thomson scattering diagnostic at ASDEX Upgrade. If these mirrors can be substituted...

Optical and additional radio data are presented for the bright galaxies of the Disney and Wall survey (1977 Mon. Not. R. Astron. Soc. 179, 235). These data form the basis of a statistical comparison of the properties of radio elliptical galaxies to radio-quiet ellipticals. The correlations may be explained by the depth of the gravitational potential well in which the galaxy resides governing the circumstances under which an elliptical galaxy rids itself of internally produced gas. (author)

Every elliptic curve E defined over C is analytically isomorphic to C*=qZ for some q ∊ C*. Similarly, Tate has shown that if E is defined over a p-adic field K, then E is analytically isomorphic to K*=qZ for some q ∊ K . Further the isomorphism E(K) ≅ K*/qZ respects the action of the Galois group GK/K, where K is the algebraic closure of K. I will explain the construction of this isomorphism.

Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K( m) and E( m), for the standard domain of the elliptic parameter, 0 procedure to compute simultaneously three Jacobian elliptic functions, sn( u| m), cn( u| m), and dn( u| m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic argument, u, after its domain is reduced to the standard range, 0 ≤ u procedure is 25-70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K( m) is not taken into account.

In this work we suggest and discuss a microstructure of air capillaries with elliptical cross-section in a tread of glass that gives opportunity for Creation of polarization-preserving fiber with very small beat length between the fundamental modes of different polarization......In this work we suggest and discuss a microstructure of air capillaries with elliptical cross-section in a tread of glass that gives opportunity for Creation of polarization-preserving fiber with very small beat length between the fundamental modes of different polarization...

More than 25 years ago, elliptic curves over finite fields were suggested as a group in which the Discrete Logarithm Problem (DLP) can be hard. Since then many researchers have scrutinized the security of the DLP on elliptic curves with the result that for suitably chosen curves only exponential

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.

We present experimental data that show significant deviations from theoretical predictions for the location of the center of the electron momenta distribution at low values of ellipticity ε of laser light. We show that these deviations are caused by significant Coulomb focusing along the minor axis of polarization, something that is normally neglected in the analysis of electron dynamics, even in cases where the Coulomb correction is otherwise taken into account. By investigating ellipticity-resolved electron momenta distributions in the plane of polarization, we show that Coulomb focusing predominates at lower values of ellipticity of laser light, while Coulomb asymmetry becomes important at higher values, showing that these two complementary phenomena can be used to probe long-range Coulomb interaction at all polarizations of laser light. Our results suggest that both the breakdown of Coulomb focusing and the onset of Coulomb asymmetry are linked to the disappearance of Rydberg states with increasing ellipticity.

In our recent paper (2010 Phys. Rev. A 82 023412) we introduced a theory of high-order harmonic generation by diatomic molecules exposed to an ellipticallypolarized laser field and have shown that the nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we now develop a theoretical approach for calculating ellipticity and the offset angle of high harmonics. We show that the emitted harmonics generated by aligned molecules are ellipticallypolarized even if the applied field is linearly polarized. Using examples of N 2 , O 2 and Ar 2 molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment and explain them by the destructive two-centre interference. Taking into account that the aligned molecules are an anisotropic medium for high harmonic generation, we introduce elliptic dichroism as a measure of this anisotropy, for both components of the T-matrix element. We propose that the measurement of the elliptic dichroism may reveal further information about the molecular structure.

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Current research into holography is concerned with applications in optically storing, retrieving, and processing information. Polarization holography has many unique properties compared to conventional holography. It gives results in high efficiency, achromaticity, and special polarization...... properties. This books reviews the research carried out in this field over the last 15 years. The authors provide basic concepts in polarization and the propagation of light through anisotropic materials, before presenting a sound theoretical basis for polarization holography. The fabrication...... and characterization of azobenzene based materials, which remain the most efficient for the purpose, is described in detail. This is followed by a description of other materials that are used in polarization holography. An in-depth description of various applications, including display holography and optical storage...

The EMW at the BESSRC beam lines at the APS provides high photon flux at high energies with the capability of producing circular polarization on axis. The authors observe a high degree of circularly polarized x-rays at such energies. The polarization and frequency tunability of the elliptical multipole wiggler (EMW) is an ideal source for many magnetic measurements from X-ray Magnetic Circular Dichroism (XMCD) to Compton scattering experiments. They performed Compton scattering measurements to determine the polarization and photon flux at the sample as a function of the deflection parameters K y and K x . They used for their measurements a Si (220) Laue monochromator providing simultaneous photon energies at 50 keV, 100 keV and 150 keV. Magnetic Compton Profiles were determined by either switching the magnet polarity or the photon helicity. The results obtained using Fe(110) single crystals were very similar

The main part of this thesis consists of 15 published papers, in which the numerical Beam Propagating Method (BPM) is investigated, verified and used in a number of applications. In the introduction a derivation of the nonlinear Schroedinger equation is presented to connect the beginning of the soliton papers with Maxwell's equations including a nonlinear polarization. This thesis focuses on the wide use of the BPM for numerical simulations of propagating light and particle beams through different types of structures such as waveguides, fibers, tapers, Y-junctions, laser arrays and crystalline solids. We verify the BPM in the above listed problems against other numerical methods for example the Finite-element Method, perturbation methods and Runge-Kutta integration. Further, the BPM is shown to be a simple and effective way to numerically set up the Green's function in matrix form for periodic structures. The Green's function matrix can then be diagonalized with matrix methods yielding the eigensolutions of the structure. The BPM inherent transverse periodicity can be untied, if desired, by for example including an absorptive refractive index at the computational window edges. The interaction of two first-order soliton pulses is strongly dependent on the phase relationship between the individual solitons. When optical phase shift keying is used in coherent one-carrier wavelength communication, the fiber attenuation will suppress or delay the nonlinear instability. (orig.)

A contribution to the theory of ellipticalpolarization in the Moessbauer effect for transitions between mixed nuclear states is reported. A relation between the two-dimensional complex vector parameterization and the photon polarization density matrix was used in describing changes in the polarization of the gamma-ray involved. (A.K.)

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and ...

In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.

Multiwavelength observations of elliptical galaxies are reviewed, with an emphasis on their implications for theoretical models proposed to explain the origin and evolution of the interstellar matter. Particular attention is given to interstellar matter at T less than 100 K (atomic and molecular gas and dust), gas at T = about 10,000 K, and gas at T = 10 to the 6th K or greater. The data are shown to confirm the occurrence of mass loss from evolved stars, significant accretion from companion galaxies, and cooling inflows; no evidence is found for large mass outflow from elliptical galaxies.

We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of radial and elliptic flow. We show that at high energies elliptic flow is generated only during the initial stages of the expansion while radial flow continues to grow until freeze-out. Quantitative comparisons with SPS data from semiperipheral Pb+Pb collisions suggest the applicability of hydrodynamical concepts already $\\approx$ 1 fm/c after impact.

Elliptic net is a generalization of elliptic divisibility sequence and in cryptography field, most cryptographic pairings that are based on elliptic curve such as Tate pairing can be improved by applying elliptic nets algorithm. The elliptic net is constructed by using n dimensional array of values in rational number satisfying nonlinear recurrence relations that arise from elliptic divisibility sequences. The two main properties hold in the recurrence relations are for all positive integers m>n, hm +nhm -n=hm +1hm -1hn2-hn +1hn -1hm2 and hn divides hm whenever n divides m. In this research, we discuss elliptic divisibility sequence associated with elliptic nets based on cryptographic perspective and its possible research direction.

Using a generalized Poincare inequality, we study the coercive properties of a class of elliptic-parabolic partial differential equations, which contains many degenerate elliptic equations considered by the other authors. (author). 16 refs

Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational (complex) and the elliptic (i.e., doubly

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

The relationship of the color gradients within ellipticals and the color differences between them are studied. It is found that the local color appears to be strongly related to the escape velocity. This suggests that the local escape velocity is the primary factor that determines the metallicity of the stellar population. Models with and without dark halos give comparable results. 27 refs

Using an improved Sobolev inequality we study a class of elliptic operators which is degenerate inside the domain and strongly degenerate near the boundary of the domain. Our results are applicable to the L 2 -boundary value problem and the mixed boundary problem. (author). 18 refs

The elliptical shape of the Coma cluster is examined quantitatively. The degree of ellipticity is high and depends to some extent on the radial distance of the sample from the Coma center as well as on the brightness of the sample. The elliptical shape does not appear to be caused by rotation; other possible causes are briefly discussed

Using a weighted Poincare inequality, we study (ω 1 ,...,ω n )-elliptic operators. This method is applicable to solve singular elliptic equations with conditions in W 1,2 on the boundary. We also get a result about the regularity of solutions of singular elliptic equations. An application to (ω 1 ,...ω n )-parabolic equations is given. (author). 33 refs

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages, like Magma. This book is suitable for students in mathematics, as well as professional mathematicians.

The effect of a polarization structure of electromagnetic radiation on the germinating capacity of seeds of such weeds as Green foxtail (Setaria viridis) and Green amaranth (Amaranthus retroflexus) has been studied. Seeds have been exposed to impulse electromagnetic radiation in a frequency of 896 MHz with linear, elliptical right-handed and elliptical left-handed polarizations at different power flux density levels. It is determined that the effect of the right-handed polarized electromagnetic radiation increases and the influence of the left-handed polarized one reduces the germinating capacity of seeds compared to the effect of the linearly polarized electromagnetic radiation. It is shown that the seeds have an amplitude polarization selectivity as evinced by the major effect of the right-handed polarized radiation on seeds. An electrodynamic model as the right-handed ellipticallypolarized antenna with the given quantity of the ellipticity of polarization is suggested to use in description of this selectivity.

We measure photoelectron angular distributions of noble gases in intense ellipticallypolarized laser fields, which indicate strong structure-dependent Coulomb asymmetry. Using a dedicated semiclassical model, we have disentangled the contribution of direct ionization and multiple forward scattering on Coulomb asymmetry in elliptical laser fields. Our theory quantifies the roles of the ionic potential and initial transverse momentum on Coulomb asymmetry, proving that the small lobes of asymmetry are induced by direct ionization and the strong asymmetry is induced by multiple forward scattering in the ionic potential. Both processes are distorted by the Coulomb force acting on the electrons after tunneling. Lowering the ionization potential, the relative contribution of direct ionization on Coulomb asymmetry substantially decreases and Coulomb focusing on multiple rescattering is more important. We do not observe evident initial longitudinal momentum spread at the tunnel exit according to our simulation.

We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference (ΔJ z =±1) excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms

Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of non-linearity and diffraction on wave propagation of optical beam in a homogeneous bulk Kerr-medium is presented. Particular emphasis is put on the variation of beam width and longitudinal phase delay with the ...

Different evolutionnary models for elliptical and lenticular galaxies are discussed. In the first part, we show that, at least some peculiar early types galaxies exhibit some activity. Then we describe the observationnal constraints: the color-magnitude diagram, the color gradient and the high metallicity of intraclusters gas. Among the different models, only the dissipation collapse followed by a hot wind driven by supernovae explosion explain in a natural way these constraints. Finally, the origin of SO is briefly discussed [fr

In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves

Neutron scattering with polarization analysis is an indispensable tool for the investigation of novel materials exhibiting electronic, magnetic, and orbital degrees of freedom. In addition, polarized neutrons are necessary for neutron spin precession techniques that path the way to obtain extremely high resolution in space and time. Last but not least, polarized neutrons are being used for fundamental studies as well as very recently for neutron imaging. Many years ago, neutron beam lines were simply adapted for polarized beam applications by adding polarizing elements leading usually to unacceptable losses in neutron intensity. Recently, an increasing number of beam lines are designed such that an optimum use of polarized neutrons is facilitated. In addition, marked progress has been obtained in the technology of 3 He polarizers and the reflectivity of large-m supermirrors. Therefore, if properly designed, only factors of approximately 2-3 in neutron intensity are lost. It is shown that S-benders provide neutron beams with an almost wavelength independent polarization. Using twin cavities, polarized beams with a homogeneous phase space and P>0.99 can be produced without significantly sacrificing intensity. It is argued that elliptic guides, which are coated with large m polarizing supermirrors, provide the highest flux.

In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.

Statistical tests for intrinsic shapes of elliptical galaxies have given so far inconclusive and sometimes contradictory results. These failures have been often charged to the fact that classical tests consider only the two axisymmetric shapes (oblate versus prolate), while ellipticals are truly triaxial bodies. On the other hand, recent analyses indicate that the class of elliptical galaxies could be a mixture of (at least) two families having different morphology and dynamical behaviour: (i) a family of fast-rotating, disc-like ellipticals (discy); (ii) a family of slow-rotating, box-shaped ellipticals (boxy). In this paper we review the tests for instrinsic shapes of elliptical galaxies using data of better quality (CCD) with respect to previous applications. (author)

We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

In a sample of 132 bright elliptical galaxies it is shown that there is a strong correlation between radio activity and flattening in the sense that radio ellipticals are both apparently and inherently rounder than the average elliptical. Both extended and compact sources are subject to the same correlation. No galaxies with axial ratios below 0.65 are found to be radio emitters. (author)

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson).

Full Text Available Doppler radar observations have revealed a class of atmospheric vortices (tropical cyclones, tornadoes, dust devils that possess elliptical radar reflectivity signatures. One famous example is Typhoon Herb (1996 that maintained its elliptical reflectivity structure over a 40-hour period. Theoretical work and dual-Doppler analyses of observed tropical cyclones have suggested two physical mechanisms that can explain the formation of two types of elliptical vortices observed in nature, namely, the combination of a circular vortex with either a wavenumber two vortex Rossby wave or a deformation field. The characteristics of these two types of elliptical vortices and their corresponding Doppler velocity signatures have not been previously examined.

We present measurements of the shape of the stellar line-of-sight velocity distribution out to two effective radii along the major axes of the four elliptical galaxies NGC 2434, 2663, 3706, and 5018. The velocity dispersion profiles are flat or decline gently with radius. We compare the data to the predictions of f = f(E, L(sub z)) axisymmetric models with and without dark matter. Strong tangential anisotropy is ruled out at large radii. We conclude from our measurements that massive dark halos must be present in three of the four galaxies, while for the fourth galaxy (NGC 2663) the case is inconclusive.

The R1/n law for the radial surface brightness of elliptical galaxies and the "Best Accretion Model" together with the "Concentration Model" have been combined in order to determine the mass and dynamical structure of largely-populated star systems. Families of models depending on four parameters have been used to fit the observed surface radial profiles of some spectro-photometric indices of a sample of eleven galaxies. We present the best agreements of the spectral index Mg2 with observations for three selected galaxies representative of the full sample. For them we have also computed the spatial distributions of the metal abundances, which are essential to achieve a population synthesis.

ABSTRACT This Chapter has the objectives to search, through the review of the available literature, important informations on the evolution of mango propagation regarding theoretical and practical aspects from cellular base of sexual propagation, nursery structures and organizations, substrate compositions and uses, importance of rootstock and scion selections, also it will be described the preparation and transport of the grafts (stem and bud) as well as the main asexual propagation methods...

{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

An overview is given of what we know about the frequency of kinematically decoupled cores in dwarf elliptical galaxies. New observations show that kinematically decoupled cores happen just as often in dwarf elliptical as in ordinary early-type galaxies. This has important consequences for the

From the generalized Yang-Baxter relations RLL=LLR*, where R and R* are the dynamical R-matrix of A n-1 (1) type face model with the elliptic module shifted by the center of the algebra, using the Ding-Frenkel correspondence, the authors obtain the Drinfeld currents of dynamical elliptic algebra

We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also partially break the supersymmetry. In spite of the regularization, one can establish a homotopy of the elliptic genus in a coupling parameter. Our construction relies on a priori estimates and other methods from constructive quantum field theory; this mathematical underpinning allows us to justify evaluating the elliptic genus at one endpoint of the homotopy. We obtain a version of Witten's proposed formula for the elliptic genus in terms of classical theta functions. As a consequence, the elliptic genus has a hidden SL(2,Z) symmetry characteristic of conformal theory, even though the underlying theory is not conformal. (orig.)

Multicolor two-dimensional surface photometry was used to obtain radial profiles for surface brightness, color, ellipticity, position angle, and the residuals from the fitted ellipses described by the cos(n phi) and sin(n phi) terms (where n = 3 and 4) for 17 elliptical galaxies. It is found that at radii as large as five times the seeing FWHM, seeing can affect the ellipticity at the 10 percent level and introduce uncertainty in the position angles of several degrees, particularly for very round ellipticals. The present profiles are found to agree well with previous data, with rms differences of 0.02 in ellipticity and 2 deg in position angle. The observed color gradients are consistent with a decrease in the metallicity by a factor of about 2 per decade in radius. 61 refs

The elliptical (fusiform) excision is a basic tool of cutaneous surgery. To assess the design, functionality, ease of construction, and aesthetic outcomes of the ellipse. A systematic review of elliptical designs and their site-specific benefits and limitations. In particular, we consider the (1). context of prevailing relaxed skin tension lines and tissue laxity; and (2). removal of the smallest possible amount of tissue around the lesion and in the "dog-ears." Attention is focused on intuitive methods that can be reproducibly planned and executed. Elliptical variations are easily designed and can be adapted to many situations. The eccentric parallelogram excision is offered as a new technique that minimizes notching and focal tension in the center of an elliptical closure. Conclusion The elliptical (fusiform) excision is an efficient, elegant, and versatile technique that will remain a mainstay of the cutaneous surgical armamentarium.

A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

Full Text Available Wave propagation in heat conducting thermo elastic plate of elliptical cross-section is studied using the Fourier expansion collocation method based on Suhubi's generalized theory. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of elliptical cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by using the boundary conditions along outer and inner surface of elliptical cross-sectional plate using Fourier expansion collocation method. The computed non-dimensional frequency, velocity and quality factor are plotted in dispersion curves for longitudinal and flexural (symmetric and antisymmetric modes of vibrations.

Two new analytic element solutions are presented for steady flow problems with elliptical boundaries. The first solution concerns groundwater flow to shallow elliptical lakes with leaky lake beds in a single-aquifer. The second solution concerns groundwater flow through elliptical cylinder inhomogeneities in a multi-aquifer system. Both the transmissivity of each aquifer and the resistance of each leaky layer may differ between the inside and the outside of an inhomogeneity. The elliptical inhomogeneity may be bounded on top by a shallow elliptical lake with a leaky lake bed. Analytic element solutions are obtained for both problems through separation of variables of the Laplace and modified-Helmholtz differential equations in elliptical coordinates. The resulting equations for the discharge potential consist of infinite sums of products of exponentials, trigonometric functions, and modified-Mathieu functions. The series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately, but up to machine accuracy provided enough terms are used. The head and flow may be computed analytically at any point in the aquifer. Examples are given of uniform flow through an elliptical lake, a well pumping near two elliptical lakes, and uniform flow through three elliptical inhomogeneities in a multi-aquifer system. Mathieu functions may be applied in a similar fashion to solve other groundwater flow problems in semi-confined aquifers and leaky aquifer systems with elliptical internal or external boundaries.

Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying q-analogues. Recently Schlosser proposed a lattice path model in the square lattice with a family of totally elliptic weight-functions including several complex parameters and discussed an elliptic extension of the binomial theorem. In the present paper, we introduce a family of discrete-time excursion processes on Z starting from the origin and returning to the origin in a given time duration 2 T associated with Schlosser's elliptic combinatorics. The processes are inhomogeneous both in space and time and hence expected to provide new models in non-equilibrium statistical mechanics. By numerical calculation we show that the maximum likelihood trajectories on the spatio-temporal plane of the elliptic excursion processes and of their reduced trigonometric versions are not straight lines in general but are nontrivially curved depending on parameters. We analyze asymptotic probability laws in the long-term limit T → ∞ for a simplified trigonometric version of excursion process. Emergence of nontrivial curves of trajectories in a large scale of space and time from the elementary elliptic weight-functions exhibits a new aspect of elliptic combinatorics.

An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.

The paper deals with issues related to the construction of solutions, 2 π-periodic in the angular variable, of the Mathieu differential equation for the circular elliptic cylinder harmonics, the associated characteristic values, and the azimuthal numbers needed to form the elementary elliptic cylinder wave functions. A superposition of the latter is one possible form for representing the analytic solution of the thermoelastic wave propagation problem in long waveguides with elliptic cross-section contour. The classical Sturm-Liouville problem for the Mathieu equation is reduced to a spectral problem for a linear self-adjoint operator in the Hilbert space of infinite square summable two-sided sequences. An approach is proposed that permits one to derive rather simple algorithms for computing the characteristic values of the angular Mathieu equation with real parameters and the corresponding eigenfunctions. Priority is given to the application of the most symmetric forms and equations that have not yet been used in the theory of the Mathieu equation. These algorithms amount to constructing a matrix diagonalizing an infinite symmetric pentadiagonal matrix. The problem of generalizing the notion of azimuthal number of a wave propagating in a cylindrical waveguide to the case of elliptic geometry is considered. Two-sided mutually refining estimates are constructed for the spectral values of the Mathieu differential operator with periodic and half-periodic (antiperiodic) boundary conditions.

Full Text Available ABSTRACT This Chapter has the objectives to search, through the review of the available literature, important informations on the evolution of mango propagation regarding theoretical and practical aspects from cellular base of sexual propagation, nursery structures and organizations, substrate compositions and uses, importance of rootstock and scion selections, also it will be described the preparation and transport of the grafts (stem and bud as well as the main asexual propagation methods their uses and practices. Finally, pattern and quality of graft mangos and their commercialization aspects will be discussed in this Chapter.

Full text: (author)Elliptic hypergeometric functions were discovered around ten years ago. They represent the top level known generalization of the Euler beta integral and Euler-Gauss 2 F 1 hypergeometric function. In general form they are defined by contour integrals involving elliptic gamma functions. We outline the structure of the simplest examples of such functions and discuss their relations to the representation theory of the classical Lie groups and their various deformations. In one of the constructions elliptic hypergeometric integrals describe purely group-theoretical objects having the physical meaning of superconformal indices of four-dimensional supersymmetric gauge field theories

This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

The transformation optics technique is employed in this paper to design two optical devices - a two-dimensional polarization splitter and a three-dimensional polarization rotator for propagating beams. The polarization splitter translates the TM- and the TE-polarized components of an incident beam in opposite directions (i.e., shifted up or shifted down). The polarization rotator rotates the polarization state of an incoming beam by an arbitrary angle. Both optical devices are reflectionless at the entry and exit interfaces. Design details and full-wave simulation results are provided.

Ellipticallypolarized magnetic fields induce higher currents in the body compared with their plane polarized counterparts. This investigation examines the degree of vector ellipticity of extremely low frequency magnetic fields (ELF-MFs) in the home, with regard to the adverse health effects reportedly associated with ELF-MFs, for instance childhood leukaemia. Tri-axial measurements of the magnitude and phase of the 0-3000 Hz magnetic fields, produced by 226 domestic mains-fed appliances of 32 different types, were carried out in 16 homes in Worcestershire in the summer of 2004. Magnetic field strengths were low, with average (RMS) values of 0.03 ± 0.02 µT across all residences. In contrast, background field ellipticities were high, on average 47 ± 11%. Microwave and electric ovens produced the highest ellipticities: mean respective values of 21 ± 21% and 21 ± 17% were observed 20 cm away from these appliances. There was a negative correlation between field strength and field polarization, which we attribute to the higher relative field contribution close to each individual (single-phase) appliance. The measurements demonstrate that domestic magnetic fields are extremely complex and cannot simply be characterized by traditional measurements such as time-weighted average or peak exposure levels. We conclude that ellipticity should become a relevant metric for future epidemiological studies of health and ELF-MF exposure. This work is supported by the charity CHILDREN with LEUKAEMIA, registered charity number 298405.

Ellipticallypolarized magnetic fields induce higher currents in the body compared with their plane polarized counterparts. This investigation examines the degree of vector ellipticity of extremely low frequency magnetic fields (ELF-MFs) in the home, with regard to the adverse health effects reportedly associated with ELF-MFs, for instance childhood leukaemia. Tri-axial measurements of the magnitude and phase of the 0-3000 Hz magnetic fields, produced by 226 domestic mains-fed appliances of 32 different types, were carried out in 16 homes in Worcestershire in the summer of 2004. Magnetic field strengths were low, with average (RMS) values of 0.03 ± 0.02 μT across all residences. In contrast, background field ellipticities were high, on average 47 ± 11%. Microwave and electric ovens produced the highest ellipticities: mean respective values of 21 ± 21% and 21 ± 17% were observed 20 cm away from these appliances. There was a negative correlation between field strength and field polarization, which we attribute to the higher relative field contribution close to each individual (single-phase) appliance. The measurements demonstrate that domestic magnetic fields are extremely complex and cannot simply be characterized by traditional measurements such as time-weighted average or peak exposure levels. We conclude that ellipticity should become a relevant metric for future epidemiological studies of health and ELF-MF exposure

This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

In the first part of this paper, we construct mod 2 elliptic genera on manifolds of dimensions 8k+1, 8k+2 by mod 2 index formulas of Dirac operators. They are given by mod 2 modular forms or mod 2 automorphic functions. We also obtain an integral formula for the mod 2 index of the Dirac operator. As a by-product we find topological obstructions to group actions. In the second part, we construct higher elliptic genera and prove some of their rigidity properties under group actions. In the third part we write down characteristic series for all Witten genera by Jacobi theta-functions. The modular property and transformation formulas of elliptic genera then follow easily. We shall also prove that Krichever's genera, which come from integrable systems, can be written as indices of twisted Dirac operators for SU-manifolds. Some general discussions about elliptic genera are given. (orig.)

Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse $\\ell$-adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforward properties: cyclotomic determinant, finite ramification, rational traces of Frobenius, and somewhere not potentially good reduction. We prove that any lisse sheaf of rank two possessing these properties comes from an elliptic curve.

This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L{sup p}-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.

We further study the elliptic genus of the cigar SL(2,ℝ){sub k}/U(1) coset superconformal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar’s throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have important consequences for the physics near horizons, even for parametrically large black holes.

Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con......For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic

The technological and metallurgical requirements of material for high-gradient superconducting cavities are described. High-purity niobium, as the preferred metal for the fabrication of superconducting accelerating cavities, should meet exact specifications. The content of interstitial impurities such as oxygen, nitrogen, and carbon must be below 10 μg g-1. The hydrogen content should be kept below 2 μg g-1 to prevent degradation of the quality factor (Q-value) under certain cool-down conditions. The material should be free of flaws (foreign material inclusions or cracks and laminations) that can initiate a thermal breakdown. Traditional and alternative cavity mechanical fabrication methods are reviewed. Conventionally, niobium cavities are fabricated from sheet niobium by the formation of half-cells by deep drawing, followed by trim machining and electron beam welding. The welding of half-cells is a delicate procedure, requiring intermediate cleaning steps and a careful choice of weld parameters to achieve full penetration of the joints. A challenge for a welded construction is the tight mechanical and electrical tolerances. These can be maintained by a combination of mechanical and radio-frequency measurements on half-cells and by careful tracking of weld shrinkage. The main aspects of quality assurance and quality management are mentioned. The experiences of 800 cavities produced for the European XFEL are presented. Another cavity fabrication approach is slicing discs from the ingot and producing cavities by deep drawing and electron beam welding. Accelerating gradients at the level of 35-45 MV m-1 can be achieved by applying electrochemical polishing treatment. The single-crystal option (grain boundary free) is discussed. It seems that in this case, high performance can be achieved by a simplified treatment procedure. Fabrication of the elliptical resonators from a seamless pipe as an alternative is briefly described. This technology has yielded good

We discuss the dispersion relation of linearly-polarized waves, propagating along a strong background magnetic field embedded in an electron-positron plasma. The results are then applied to the study of the propagation conditions of coherent curvature radio radiation inside neutron stars magnetospheres, as produced by electric discharges following current pulsar models.

We examine the properties of an ellipticallypolarized wiggler that will generate circularly polarized photons with energy spectrum of 3--12 KeV. The vertical wiggler magnetic field is produced by permanent magnets while the horizontal wiggler field is generated by electric coils capable of AC excitation. The radiation parameters of the wiggler is discussed. We consider AC excitation of the wiggler to produce the time modulation of the ellipticpolarization. The power is dissipated in the vacuum chamber due to the eddy current

The temporal evolution of photoinduced birefringence is investigated on the basis of a model proposed by Pedersen and co-workers, This model is extended for the case of ellipticallypolarized light, and used to describe the erasure of photoinduced birefringence by circularly polarized light...

We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~0.5" resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are ``ellipticals in formation.'' Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrotsini/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history. Based on observations at the European Southern Observatory, Chile (ESO 65.N-0266, 65.N-0289), and on observations at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, The University of California, and the National Aeronautics and Space Administration. The Keck Observatory was made possible by the general financial support by the W. M. Keck Foundation.

We consider polarization states of three photons, propagating collinearly and having equal given frequencies but with arbitrary distributed horizontal or vertical polarizations of photons. A general form of such states is a superposition of four basic three-photon polarization modes, to be referred to as the three-photon polarization ququarts (TPPQ). All such states can be considered as consisting of one- and two-photon parts, which can be entangled with each other. The degrees of entanglement and polarization, as well as the Schmidt decomposition and Stokes vectors of TPPQ are found and discussed. (paper)

Based on a number of new discoveries resulting from 10 years of Chandra and XMM-Newton observations and corresponding theoretical works, this is the first book to address significant progress in the research of the Hot Interstellar Matter in Elliptical Galaxies. A fundamental understanding of the physical properties of the hot ISM in elliptical galaxies is critical, because they are directly related to the formation and evolution of elliptical galaxies via star formation episodes, environmental effects such as stripping, infall, and mergers, and the growth of super-massive black holes. Thanks to the outstanding spatial resolution of Chandra and the large collecting area of XMM-Newton, various fine structures of the hot gas have been imaged in detail and key physical quantities have been accurately measured, allowing theoretical interpretations/predictions to be compared and tested against observational results. This book will bring all readers up-to-date on this essential field of research.

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

In this paper it is continued the behavior analysis and comparison between cylindrical fuel rods of circular and elliptical cross sections. Taking into account the accepted models in the literature, the fission gas swelling and release were studied. An analytical comparison between both kinds of rod reveals a sensible gas release reduction in the elliptical case, a 50% swelling reduction due to intragranular bubble coalescence mechanism and an important swelling increase due to migration bubble mechanism. From the safety operation point of view, for the same linear power, an elliptical cross section rod is favored by lower central temperatures, lower gas release rates, greater gas store in ceramic matrix and lower stored energy rates. (author). 6 refs., 8 figs., 1 tab

Structures with unique electromagnetic properties are designed based on the approach of spatial coordinate transformations of Maxwell's equations. This approach is applied to scheme out invisible elliptic cylinder cloaks, which provide more feasibility for cloaking arbitrarily shaped objects. The transformation expressions for the anisotropic material parameters and the field distribution are derived. The cloaking performances of ideal and lossy elliptic cylinder cloaks are investigated by finite element simulations. It is found that the cloaking performance will degrade in the forward direction with increasing loss. (fundamental areas of phenomenology (including applications))

We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from

We determine abundance ratios of 37 dwarf ellipticals (dEs) in the nearby Virgo cluster. This sample is representative of the early-type population of galaxies in the absolute magnitude range -19.0 originate from late-type dwarfs or small spirals. Na-yields appear to be very metal-dependent, in agreement with studies of giant ellipticals, probably due to the large dependence on the neutron-excess in stars. We conclude that dEs have undergone a considerable amount of chemical evolution, they are therefore not uniformly old, but have extended SFH, similar to many of the Local Group galaxies.

The book on 'polarized neutrons' is intended to inform researchers in condensed matter physics and chemistry of the diversity of scientific problems that can be investigated using polarized neutron beams. The contents include chapters on:- neutron polarizers and instrumentation, polarized neutron scattering, neutron polarization analysis experiments and precessing neutron polarization. (U.K.)

An extension of the beam-deflection method to the case of elliptical preforms with eccentric core (asymmetrical elliptical preforms) is presented, which can be easily implemented on automatic measurement equipment

This paper discusses the basic properties of various versions of the two-variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the theories regarding the elliptic genera of phases on N = 2 introduced in Witten (1993 Nucl. Phys. B 403 159-222).

The wake fields of a bunched beam caused by the resistivity of the chamber walls are investigated for a vacuum chamber with elliptical cross section. The longitudinal and transverse impedances are calculated for arbitrary energies and for an arbitrary position of the beam in the chamber. (orig.)

We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270-8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range.

A Carleman estimate for a certain first order elliptic system is proved. The proof is elementary and does not rely on pseudo-differential calculus. This estimate is used to prove Carleman estimates for the isotropic Lame system as well as for the isotropic Maxwell system with C 1 coefficients

The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in SatScan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic...

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

Highlights: • A general form for the magnetostatic energy is calculated for the vortex state in a ferromagnetic ellipse. • The ellipse magnetostatic energy is minimized by conformal mapping the circular disk onto the ellipse. • The gyrotropic precession frequency is obtained in general for a range of ellipticities. - Abstract: The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk. It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.

The aim of this study is to determine abundance ratios and star formation histories (SFH) of dwarf ellipticals in the nearby Virgo cluster. We perform a stellar population analysis of 39 dEs and study them using index-index and scaling relations. We find an unusual behaviour where [Na/Fe] is

The risks of buckling of dished vessel head increase when the vessel is thin walled. This paper gives the last results on experimental tests of 3 elliptical heads and compares all the results with some empirical formula dealing with elastic and plastic buckling

This paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast

systematize the local identities by deriving four local 'master identities' analogous to the ... involving Jacobi elliptic functions can be explicitly evaluated and a number of .... most of these integrals do not seem to be known in the literature. In §6 ...

The complete description of the polarization of a beam of radiation is described in terms of the total energy and three polarization rates. The polarization characteristics from conventional undulators and wigglers is recalled. A presentation is made of some new insertion devices that were proposed and/or built to generate circular polarization and more generally to improve the control of polarization. They are the asymmetric and elliptical wigglers and the helical and crossed undulators

We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure mathematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals, and we develop a formalism that enables us to compute these Feynman integrals in terms of our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.

New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models

We analyze elliptic ﬂow from SIS to RHIC energies systematically in a realistic dynamical cascade model. We compare our results with the recent data from STAR and PHOBOS collaborations on elliptic ﬂow of charged particles at midrapidity in Au + Au collisions at RHIC. In the analysis of elliptic ﬂow at RHIC energy, we ﬁnd ...

and a single layer with a ground plane can have 100 % polarization conversion efficiency. We tested our conclusions numerically reaching the designated limits of efficiency using a simple metamaterial design. Our general analysis provides useful guidelines for the metamaterial polarization converter design......In this paper, we analyze the theoretical limits of a metamaterial-based converter with orthogonal linear eigenpolarizations that allow linear-to-ellipticalpolarization transformation with any desired ellipticity and ellipse orientation. We employ the transmission line approach providing a needed...... level of the design generalization. Our analysis reveals that the maximal conversion efficiency for transmission through a single metamaterial layer is 50 %, while the realistic reflection configuration can give the conversion efficiency up to 90 %. We show that a double layer transmission converter...

Polarized neutron scattering from dynamic polarized targets has been applied to various hydrogenous materials at different laboratories. In situ structures of macromolecular components have been determined by nuclear spin contrast variation with an unprecedented precision. The experiments of selective nuclear spin depolarisation not only opened a new dimension to structural studies but also revealed phenomena related to propagation of nuclear spin polarization and the interplay of nuclear polarisation with the electronic spin system. The observation of electron spin label dependent nuclear spin polarisation domains by NMR and polarized neutron scattering opens a way to generalize the method of nuclear spin contrast variation and most importantly it avoids precontrasting by specific deuteration. It also likely might tell us more about the mechanism of dynamic nuclear spin polarisation. (author) 4 figs., refs.

Based on a pair of coupled 2D nonlinear Schrödinger equations, the collapse dynamics of a vector field with hybrid states of polarization (SoP) in a Kerr medium is demonstrated. The critical power for an optical field to collapse is present, and the full vectorial numerical simulations provide detailed information about the evolution and partial collapse of the vector field in a Kerr medium. Our results reveal that the optical field prefers to collapse in linearly-polarization, as a result of the self-focusing effect difference in linearly, elliptically and circularly polarized components. The SoP in the field cross-section changes and propagates with a spiral trajectory when the vector beams are imposed with a vortex. The vectorial effect on the collapse of a vector optical field can prevail over the noise even though it reaches 10% amplitude of the optical field. The unique feature of these structured collapses of a vector optical field may lead to new phenomena in the interaction of light with matter. (paper)

High order harmonics generated from 400 nm driving pulses hold promise of scaling photon flux of single attosecond pulses by one to two orders of magnitude. We report ellipticity dependence and phase matching of high order harmonics generated from such pulses in Neon gas target and compared them with similar measurements using 800 nm driving pulses. Based on measured ellipticity dependence, we predict that double optical gating (DOG) and generalized double optical gating (GDOG) can be employed to extract intense single attosecond pulses from pulse train, while polarization gating (PG) may not work for this purpose. This material is supported by the U.S. Army Research Office under grant number W911NF-07-1-0475, and by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy.

An automotive suspension system is designed to provide both safety and comfort for the vehicle occupants. In this study, finite element models were developed to optimize the material and geometry of the composite elliptical spring based on the spring rate, log life and shear stress parameters. The influence of the ellipticity ratio on the performance of woven roving-wrapped composite elliptical springs was investigated both experimentally and numerically. The study demonstrated that composite elliptical springs can be used for light and heavy trucks with substantial weight reduction. The results showed that the ellipticity ratio significantly influenced the design parameters. Composite elliptic springs with ellipticity ratios of a/b = 2 had the optimum spring parameters.

This paper presents some work conducted at EDF R and D Division to evaluate the probability that a semi-elliptical crack in a pipe not only initiates but also propagates when submitted to mechanical loading such as bending and pressure combined or not with a thermal shock. The first part is related to the description of the mechanical model: the simplified methods included in the French RSE-M Code used to evaluate the J-integral as well as the principle of the determination of the crack propagation. Then, the way this deterministic approach is combined to a reliability code is described. Finally, an example is shown: the initiation and the instability of a semi-elliptical crack in a pipe submitted to combined pressure and bending moment. (author)

Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics

We consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2,2) superconformal field theories in the infra-red, a prototype of which is the SL(2,ℝ)/U(1) (cigar) coset. We compute the elliptic genus of the GLSMs as a path-integral on the torus using supersymmetric localization. We find that the result is a Jacobi-like form that is non-holomorphic in the modular parameter τ of the torus, with mock modular behavior. This agrees with a previously-computed expression in the cigar coset. We show that the lack of holomorphicity of the elliptic genus arises from the contributions of a compact boson carrying momentum and winding excitations. This boson has an axionic shift symmetry and plays the role of a compensator field that is needed to cancel the chiral anomaly in the rest of the theory.

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear dampings. Comparison between approximate and numerical solutions is made for different values of the damping parameter. -- Highlights: → We study rotations of the mathematical pendulum when its pivot moves along an ellipse. → There are stable exact solutions for a circular pivot trajectory and zero gravity. → Asymptotic solutions are found for an elliptical pivot trajectory

Recent studies have shown that massive galaxies in the distant universe are surprisingly compact, with typical sizes about a factor of three smaller than equally massive galaxies in the nearby universe. It has been suggested that these massive galaxies grow into systems resembling nearby galaxies through a series of minor mergers. In this model the size growth of galaxies is an inherently stochastic process, and the resulting size-luminosity relationship is expected to have considerable environmentally dependent scatter. To test whether minor mergers can explain the size growth in massive galaxies, we have closely examined the scatter in the size-luminosity relation of nearby elliptical galaxies using a large new database of accurate visual galaxy classifications. We demonstrate that this scatter is much smaller than has been previously assumed, and may even be so small as to challenge the plausibility of the merger-driven hierarchical models for the formation of massive ellipticals.

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with Θ-winding number m = 1 and φ-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing. This solution is a regular non-BPS finite energy solution.

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented

Full Text Available We prove the existence of a nonzero solution for the fourth order elliptic equation $$Delta^2u= mu u +a(xg(u$$ with boundary conditions $u=Delta u=0$. Here, $mu$ is a real parameter, $g$ is superlinear both at zero and infinity and $a(x$ changes sign in $Omega$. The proof uses a variational argument based on the argument by Bahri-Lions cite{BL}.

In the scenario of single-field inflation, this field is described in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analyzed using the Hamilton-Jacobi approach and then the main results are contrasted with the recent measurements obtained from the Planck 2015 data. (orig.)

We examine the properties of an ellipticallypolarized wiggler that will generate circularly polarized photons with energy spectrum of 3--12 KeV. The vertical wiggler magnetic field is produced by permanent magnets while the horizontal wiggler field is generated by electric coils capable of AC excitation. The radiation parameters of the wiggler are presented, including photon flux, circular and linear polarization and spectrum. These parameters are compared to the synchrotron radiation from a bending magnet. Numerical values are calculated for radiation from the wiggler and bending magnet for the NSLS X-ray ring parameters. A conceptual design for such a wiggler is discussed and several different alternatives are analyzed. We consider AC excitation of the wiggler to produce the time modulation of the ellipticpolarization, and also to produce time modulated linearly polarized radiation

In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry of transportation models, the new model considers that the number of relationships between two locations is inversely proportional to the population in the ellipse whose foci are in these two locations. The elliptic model is evaluated by considering the anonymous communications patterns of 25 million users from three different countries, where a location has been assigned to each user based on their most used phone tower or billing zip code. With this information, spatial social networks are built at three levels of resolution: tower, city and region for each of the three countries. The elliptic model achieves a similar performance when predicting communication fluxes as transportation models do when predicting trips. This shows that human relationships are influenced at least as much by geography as is human mobility. (paper)

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational + centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes with n = 0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Young et al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical galaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

We investigate the polarization properties of below-threshold harmonics from aligned molecules in linearly polarized laser fields numerically and analytically. We focus on lower-order harmonics (LOHs). Our simulations show that the ellipticity of below-threshold LOHs depends strongly on the orientation angle and differs significantly for different harmonic orders. Our analysis reveals that this LOH ellipticity is closely associated with resonance effects and the axis symmetry of the molecule. These results shed light on the complex generation mechanism of below-threshold harmonics from aligned molecules.

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented.

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

A study of the orthogonal polarization modes crosstalk changes in the point of different mechanical actions (pressure force) in the polarization-maintaining fiber with straining elliptical cladding is presented. It was found that by increasing of the pressure force the polarization extinction ratio increases nonlinearly. Also revealed the dependence of the extinction coefficient and the angle between vector of the mechanical action and polarization axes of the test fiber, which leads to change the extinction coefficient variable from -57 dB to -25 dB under the pressure force of 0.7 N. Also it was found that the cross angle of the fiber axes doesn't influence on the extinction ratio value of the mechanical induced polarization crosstalk.

This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.

The traversal of an ellipticallypolarized optical field through a thermal vapor cell can give rise to a rotation of its polarization axis. This process, known as polarization self-rotation (PSR), has been suggested as a mechanism for producing squeezed light at atomic transition wavelengths. We ...

Design details of a Ku band metasurface (MTS) antenna with dual circularly polarized (CP) broadside radiation is shown in this work. By means of the surface impedance tensor modulation, synchronized propagation of two transversal magnetic (TM) and transverse electric (TE) surface waves (SWs) is ensured in the structure, which contribute to the radiation in broadside direction by the generation of a CP leaky wave. The structure is implemented by elliptical subwavelength metallic elements with a cross-shaped aperture in the center, printed on top of a thin substrate with high permittivity (AD1000 with a thickness of λ0/17). For the experimental validation, the MTS prototype has been excited employing an orthomode transducer composed by a metallic stepped septum inside an air-filled waveguide. Two orthogonal TE11 modes excited with ±90° phase shift in the feed couple with the TM and TE SWs supported by the MTS and generate RHCP or LHCP broadside beam. Experimental results are compared with the simulation predictions. Finally, conclusions are drawn.

One hundred years ago Michelson discovered circular polarization in reflection from beetles. Today a novel Mueller-matrix ellipsometry setup allows unprecedented detailed characterization of the beetles' polarization properties. A formalism based on ellipticalpolarization for description of reflection from scarab beetles is here proposed and examples are given on four beetles of different character: Coptomia laevis - a simple dielectric mirror; Cetonia aurata - a left-hand narrow-band ellipticalpolarizer; Anoplognathus aureus - a broad-band ellipticalpolarizer; and Chrysina argenteola - a left-hand polarizer for visible light at small angles, whereas for larger angles, red reflected light is right-handed polarized. We confirm the conclusion of previous studies which showed that a detailed quantification of ellipticity and degree of polarization of cuticle reflection can be performed instead of only determining whether reflections are circularly polarized or not. We additionally investigate reflection as a function of incidence angle. This provides much richer information for understanding the behaviour of beetles and for structural analysis.

Polarization of electromagnetic radiation is required very often in numerous scientific and industrial applications: studying of crystals, molecules and intermolecular interaction high-temperature superconductivity, semiconductors and their transitions, polymers and liquid crystals. Using polarized radiation allows to obtain important data (otherwise inaccessible) in astrophysics, meteorology and oceanology. It is promising in chemistry and biology for selective influence on definite parts of molecules in chain synthesis reactions, precise control of various processes at cell and subcell levels, genetic engineering etc. Though polarization methods are well elaborated in optics, they can fail in far-infrared, vacuum-ultraviolet and X-ray regions because of lack of suitable non-absorbing materials and damaging of optical elements at high specific power levels. Therefore, it is of some interest to analyse polarization of untreated FEL radiation obtained with various types of undulators, with and without axial magnetic field. The polarization is studied using solutions for electron orbits in various cases: plane or helical undulator with or without axial magnetic field, two plane undulators, a combination of right- and left-handed helical undulators with equal periods, but different field amplitudes. Some examples of how a desired polarization (elliptical circular or linear) can be obtained or changed quickly, which is necessary in many experiments, are given.

The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...

Northern Italy is a diverse geological region, including the wide and thick Po Plain sedimentary basin, which is bounded by the Alps and the Apennines. The seismically slow shallow structure of the Po Plain is difficult to retrieve with classical seismic measurements such as surface wave dispersion, yet the detailed structure of the region greatly affects seismic wave propagation and hence seismic ground shaking. Here we invert Rayleigh wave ellipticity measurements in the period range 10-60 s for 95 stations in northern Italy using a fully non linear approach to constrain vertical vS,vP and density profiles of the crust beneath each station. The ellipticity of Rayleigh wave ground motion is primarily sensitive to shear-wave velocity beneath the recording station, which reduces along-path contamination effects. We use the 3D layering structure in MAMBo, a previous model based on a compilation of geological and geophysical information for the Po Plain and surrounding regions of northern Italy, and employ ellipticity data to constrain vS,vP and density within its layers. We show that ellipticity data from ballistic teleseismic wave trains alone constrain the crustal structure well. This leads to MAMBo-E, an updated seismic model of the region's crust that inherits information available from previous seismic prospection and geological studies, while fitting new seismic data well. MAMBo-E brings new insights into lateral heterogeneity in the region's subsurface. Compared to MAMBo, it shows overall faster seismic anomalies in the region's Quaternary, Pliocene and Oligo-Miocene layers and better delineates the seismic structures of the Po Plain at depth. Two low velocity regions are mapped in the Mesozoic layer in the western and eastern parts of the Plain, which seem to correspond to the Monferrato sedimentary basin and to the Ferrara-Romagna thrust system, respectively.

We study elliptic vortices on ℂ × T 2 by considering the 2d quiver gauge theory describing their moduli spaces. The elliptic genus of these moduli spaces is the elliptic version of vortex partition function of the 4d theory. We focus on two examples: the first is a N = 1, U( N ) gauge theory with fundamental and anti-fundamental matter; the second is a N = 2, U( N ) gauge theory with matter in the fundamental representation. The results are instances of 4d "holomorphic blocks" into which partition functions on more complicated surfaces factorize. They can also be interpreted as free-field representations of elliptic Virasoro algebrae.

We discuss the possibility of Mathieu group M{sub 24} acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M{sub 24} so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M{sub 24}. In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

We discuss the possibility of Mathieu group M 24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M 24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M 24 . In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

Schombert, James M., E-mail: jschombe@uoregon.edu [Department of Physics, University of Oregon, Eugene, OR 97403 (United States)

2016-12-01

Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

Photographic image-tube spectra in the wavelength interval 3400--4500 A have been obtained for 12 elliptical galaxy nuclei and for a number of Galactic globular and open clusters in integrated light. The spectra have a wavelength resolution of 2.5 A and a high signal-to-noise ratio. A new quantitative three-dimensional spectral-classification system that has been calibrated on a sample of approx.200 individual stars (Rose 1984) is used to analyze the integrated spectra of the ellipical galaxy nuclei and to compare them with those of the globular clusters. This system is based on spectral indices that are formed by comparing neighborhood spectral features and is unaffected by reddening. The following results have been found: (1) Hot stars (i.e., spectral types A and B) contribute only 2% to the integrated spectra of elliptical galaxies at approx.4000 A, except in the nucleus of NGC 205, where the hot component dominates. This finding is based on a spectral index formed from the relative central intensities in the Ca II H+Hepsilon and Ca II K lines, which is shown to be constant for late-type (i.e., F, G, and K) stars, but changes drastically at earlier types. The observed Ca II H+Hepsilon/Ca II K indices in ellipticals can be reproduced by the inclusion of a small metal-poor population (as in the globular cluster M5) that contributes approx.8% of the light at 4000 A. Such a contribution is qualitatively consistent with the amount of

Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.

This theory grant was awarded to study the curious nature, origin and evolution of hot gas in elliptical galaxies and their surrounding groups. Understanding the properties of this X-ray emitting gas has profound implications over the broad landscape of modern astrophysics: cosmology, galaxy formation, star formation, cosmic metal enrichment, galactic structure and dynamics, and the physics of hot gases containing dust and magnetic fields. One of our principal specific objectives was to interpret the marvelous new observations from the XMM and Chandru satellite X-ray telescopes.

New HI detections have been obtained using the Nancay radiotelescope for NGC 2974 and 3962. These results and the large scale distribution obtained for NGC 3962 indicate that the HI-rich elliptical galaxies exhibit common properties which are not easily explained by accretion of an intergalactic cloud. The field aroud NGC 1052 has been mapped and there is an HI connection with the neighbouring galaxies. The HI content of several IO galaxies indicates that the galaxies which are members of groups are relatively HI-rich; this could be produced by additional HI coming from companion galaxies [fr

The dispersion relation of electromagnetic waves propagating in an elliptical plasma waveguide with a cold collisionless unmagnetized plasma column and a dielectric rod is studied analytically. The frequency spectrum of the hybrid waves and the growth rate for excitation of the waves by a thin annular relativistic elliptical electron beam (TAREEB) is obtained. The effects of relative permittivity constant of dielectric rod, geometrical dimensions, plasma frequency, accelerating voltage, and current density of TAREEB on the growth rate and frequency spectra of the waveguide will be investigated.

A numerical simulation of shock propagation in a clumpy medium with a weak magnetic field is presented which illustrates a number of dynamical processes of potential importance for explaining spectral line width and radio polarization measurements in supernova remnants

Composed of ultrathin metal or dielectric nanostructures, metasurfaces can manipulate the phase, amplitude and polarization of electromagnetic waves at a subwavelength scale, which is promising for flat optical devices. In general, metasurfaces composed of space-variant anisotropic units are sensitive to the incident polarization due to the inherent polarization dependent geometric phase. Here, we implement polarization-independent broadband metasurface holograms constructed by polarization-dependent anisotropic elliptical nanoholes by elaborate design of complex amplitude holograms. The fabricated meta-hologram exhibits a polarization insensitive feature with an acceptable image quality. We verify the feasibility of the design algorithm for three-dimensional (3D) meta-holograms with simulation and the feasibility for two-dimensional (2D) meta-holograms is experimentally demonstrated at a broadband wavelength range from 405 nm to 632.8 nm. The effective polarization-independent broadband complex wavefront control with anisotropic elliptical nanoholes proposed in this paper greatly promotes the practical applications of the metasurface in technologies associated with wavefront manipulation, such as flat lens, colorful holographic displays and optical storage.

By changing the thickness of a semiconductor cladding layer deposited on a planar dielectric waveguide, the TE or TM propagating modes may be selectively attenuated. This polarization effect is due to the periodic coupling between the lossless propagating modes of the dielectric slab waveguide and the lossy modes of the cladding layer. Experimental tests involving silicon claddings show high selectivity for either polarization.

The results of numerical experiments are used to guide an analytic discussion of hyperbolic mergers among an uncorrelated galaxy population. The expected merger rate is derived as a function of progenitor mass and relative angular momentum, and is used to predict the distribution of the parameter V/sub c//sigma 0 for merger products where V/sub c/ is the maximum observed rotation velocity in a galaxy and sigma 0 is its central velocity dispersion. The median value of this parameter for mergers between comparable galaxies is estimated to be 0.65 and is higher than the observed value in any of the 14 galaxies for which data are available. It seems unlikely that most elliptical galaxies are the result of single or multiple mergers between initially unbound stellar systems; further observational and theoretical work is suggested which should lead to a conclusive test of this picture. The present arguments cannot, however, exclude formation from low angular momentum elliptical orbits

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

In this paper we present the wave propagation method for the retrieving of effective properties of media with circularly polarized eigenwaves, in particularly for chiral metamaterials. The method is applied for thick slabs and provides bulk effective parameters. Its strong sides are the absence...

We study string propagation in an exact, stringy, four-dimensional dyonic black hole background. The exact solutions in terms of elliptic functions describing string configurations in the J=0 limit are obtained by solving the string equations of motion and constraints. By using the covariant formalism, we also investigate the propagation of physical perturbations along the string in the given curved background. copyright 1997 The American Physical Society

The polarization switch of a free-electron laser (FEL) is of great importance to the user scientific community. In this paper, we investigate the generation of controllable polarization FEL from two well-known approaches for Dalian coherent light source, i.e., crossed planar undulator and elliptical permanent undulator. In order to perform a fair comparative study, a one-dimensional time-dependent FEL code has been developed, in which the imperfection effects of an elliptical permanent undulator are taken into account. Comprehensive simulation results indicate that the residual beam energy chirp and the intrinsic FEL gain may contribute to the degradation of the polarization performance for the crossed planar undulator. The elliptical permanent undulator is not very sensitive to the undulator errors and beam imperfections. Meanwhile, with proper configurations of the main planar undulators and additional elliptical permanent undulator section, circular polarized FEL with pulse energy exceeding 100 μJ could be achieved at Dalian coherent light source. (authors)

We present a detailed theoretical description of the optical properties of planar metamaterials comprising a metal membrane patterned with openings (microslots) arranged in closely located couples (dimers). Using the covariant coupled-dipole approach, the effective material tensors of such a metamaterial are recovered, and contributions responsible for elliptical dichroism and optical activity are identified. Polarization conversion properties of II-shaped and V-shaped dimers are determined and explained in terms of ellipticallypolarized eigenmodes of the metamaterial. Good agreement with direct numerical simulations is demonstrated. The results obtained are promising for the design of thin-film frequency selective polarization shapers for terahertz waves.

Topics covered in this chapter include a discussion of exact results as related to nuclear materials management and accounting in nuclear facilities; propagation of error for a single measured value; propagation of error for several measured values; error propagation for materials balances; and an application of error propagation to an example of uranium hexafluoride conversion process

We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

Flow over mountains in the stably stratified atmosphere excites gravity waves. The three-dimensional propagation of these waves into the stratosphere is studied using linear theority as well as idealized and realistic numerical simulations. Stagnation, momentum fluxes and temperature anomalies are analyzed for idealized types of flow. Isolated mountains with elliptical contours are considered. The unperturbed atmosphere has constant wind speed and constant static stability or two layers (troposphere/stratosphere) of constant stability each. Real flow over orography is investigated where gravity waves in the stratosphere have been observed. Characteristics of the gravity wave event over the southern tip of Greenland on 6 January 1992 were recorded on a flight of the ER-2 at an altitude of 20 km. In the second case polar stratospheric clouds (PSC) were observed by an airborne Lidar over Northern Scandinavia on 9 January 1997. The PSC were induced by temperature anomalies in orographic gravity waves. (orig.)

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

Elliptic Newton flows are generated by a continuous, desingularized Newton method for doubly periodic meromorphic functions on the complex plane. In the special case, where the functions underlying these elliptic Newton flows are of second-order, we introduce various, closely related, concepts of

Full Text Available In this article we show the existence of three weak solutions of a Dirichlet quasilinear elliptic system of differential equations which involves a general (p,q-elliptic operator in divergence, with $1

This paper discusses the change in the ellipticity of two-dimensional magnetization trajectories as the applied field rotates from the easy axis to the hard axis of a material. Furthermore, the impact that the reversible magnetization has on the ellipticity is discussed, including the relationship between the magnetization squareness and the reversible component of the magnetization

This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations

High-quality visual-infrared color profiles have been determined for elliptical galaxies for the first time. Surface photometry in J and K is presented for 12 bright elliptical galaxies, and the results have been combined with CCD data in visual passbands. It is shown that the galaxies become bluer

No fluctuations in polarization have been found during a 7 GHz solar burst showing 17s periodic pulses in intensity. Polarization effects can be produced by the propagation media in the active centre, which are not affected directly by the burst source, but situated more deeply than the observed heights at that microwave frequency.

Method for determining polarities of lightning strokes more than 400 km away. Two features of signal from each stroke correlated. New method based on fact each stroke observed thus far for which polarity determined unambiguously, initial polarity of tail same as polarity of initial deflection before initial-deflection signal altered by propagation effects. Receiving station equipped with electric-field-change antenna coupled to charge amplifier having time constant of order of 1 to 10 seconds. Output of amplifier fed to signal-processing circuitry, which determines initial polarity of tail.

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs...... in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance...... advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem...

Multipacting is a resonant process, where the number of unwanted electrons resulting from a parasitic discharge rapidly grows to a larger value at some specific locations in a radio-frequency cavity. This results in a degradation of the cavity performance indicators (e.g. the quality factor Q and the maximum achievable accelerating gradient Eacc), and in the case of a superconducting radiofrequency (SRF) cavity, it leads to a quenching of superconductivity. Numerical simulations are essential to pre-empt the possibility of multipacting in SRF cavities, such that its design can be suitably refined to avoid this performance limiting phenomenon. Readily available computer codes (e.g.FishPact, MultiPac,CST-PICetc.) are widely used to simulate the phenomenon of multipacting in such cases. Most of the contemporary two dimensional (2D) codes such as FishPact, MultiPacetc. are unable to detect the multipacting in elliptic cavities because they use a simplistic secondary emission model, where it is assumed that all the secondary electrons are emitted with same energy. Some three-dimensional (3D) codes such as CST-PIC, which use a more realistic secondary emission model (Furman model) by following a probability distribution for the emission energy of secondary electrons, are able to correctly predict the occurrence of multipacting. These 3D codes however require large data handling and are slower than the 2D codes. In this paper, we report a detailed analysis of the multipacting phenomenon in elliptic SRF cavities and development of a 2D code to numerically simulate this phenomenon by employing the Furman model to simulate the secondary emission process. Since our code is 2D, it is faster than the 3D codes. It is however as accurate as the contemporary 3D codes since it uses the Furman model for secondary emission. We have also explored the possibility to further simplify the Furman model, which enables us to quickly estimate the growth rate of multipacting without

Recently WMAP and BOOMERanG experiments have set stringent constraints on the polarization angle of photons propagating in an expanding universe: Δα = (−2.4±1.9)°. The polarization of the Cosmic Microwave Background radiation (CMB) is reviewed in the context of nonlinear electrodynamics (NLED). We compute the polarization angle of photons propagating in a cosmological background with planar symmetry. For this purpose, we use the Pagels-Tomboulis (PT) Lagrangian density describing NLED, which has the form L ∼ (X/Λ{sup 4}){sup δ−1} X, where X = ¼F{sub αβ}F{sup αβ}, and δ the parameter featuring the non-Maxwellian character of the PT nonlinear description of the electromagnetic interaction. After looking at the polarization components in the plane orthogonal to the (x)-direction of propagation of the CMB photons, the polarization angle is defined in terms of the eccentricity of the universe, a geometrical property whose evolution on cosmic time (from the last scattering surface to the present) is constrained by the strength of magnetic fields over extragalactic distances.

We argue that RHIC data, in particular those on the anisotropic flow coefficients v_2 and v_4, suggest that the matter produced in the early stages of nucleus-nucleus collisions is incompletely thermalized. We interpret the parameter (1/S)(dN/dy), where S is the transverse area of the collision zone and dN/dy the multiplicity density, as an indicator of the number of collisions per particle at the time when elliptic flow is established, and hence as a measure of the degree of equilibration. This number serves as a control parameter which can be varied experimentally by changing the system size, the centrality or the beam energy. We provide predictions for Cu-Cu collisions at RHIC as well as for Pb-Pb collisions at the LHC.

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

A numerical approach to nonlinear propagation in waveguides based on real-space Gaussian quadrature integration of the nonlinear polarization during propagation is investigated and compared with the more conventional approach based on expressing the nonlinear polarization by a sum of mode overlap...

Recent developments in laser-driven photoemission sources of polarized electrons have made prospects for highly polarized electron beams in a future linear collider very promising. This talk discusses the experiences with the SLC polarized electron source, the recent progress with research into gallium arsenide and strained gallium arsenide as a photocathode material, and the suitability of these cathode materials for a future linear collider based on the parameters of the several linear collider designs that exist

In the course of an experiment to modify the ionosphere, the direction of pump wave propagation is affected by density gradients in the horizontal and vertical directions, fundamentally affecting wave-energy transport. Horizontal gradients on various scales may await a modification attempt as a preexisting state of the ionosphere and/or be changed by the deposition of heater radio-frequency energy. In the results from the Radio Receiver Instrument (RRI) in the enhanced Polar Outflow Probe (e-POP), we have recorded on the order of 100 flights over ionospheric heaters revealing a variety of processes that high-frequency pump waves experience in the ionosphere. E-POP flies on the Canadian satellite CASSIOPE in an elliptic (320 x 1400 km), highly-inclined (81°) orbit. High frequency measurements have been/are being made near SPEAR, HAARP, Sura, EISCAT Heating and Arecibo. Electromagnetic waves from ground-based heaters are detected by the two, orthogonal, 6-m dipoles on the RRI. The high input impedance of the RRI means that the dipoles act as voltage probes, from which the electric field of incoming waves can be simply computed. When combined with cold-magnetoplasma electric-field theory, the relationship of voltages on the two orthogonal dipoles is used to deduce the direction of arrival of an incoming wave in three dimensions. We illustrate the technique by its application to analysis of signals from different transmitters. These results show a variety of pump-wave propagation directions, indicating the complexity of density structure within which modification might take place. Such complexity illustrates the importance of three-dimensional models of density in the vicinity of modification.

Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

In previous papers, early whistler propagation measurements were presented [W. E. Amatucci et al., IEEE Trans. Plasma Sci. 33, 637 (2005)] as well as antenna impedance measurements [D. D. Blackwell et al., Phys. Plasmas 14, 092106 (2007)] performed in the Naval Research Laboratory Space Physics Simulation Chamber (SPSC). Since that time there have been major upgrades in the experimental capabilities of the laboratory in the form of improvement of both the plasma source and antennas. This has allowed access to plasma parameter space that was previously unattainable, and has resulted in measurements that provide a significantly clearer picture of whistler propagation in the laboratory environment. This paper presents some of the first whistler experimental results from the upgraded SPSC. Whereas previously measurements were limited to measuring the cyclotron resonance cutoff and ellipticalpolarization indicative of the whistler mode, now it is possible to experimentally plot the dispersion relation itself. The waves are driven and detected using balanced dipole and loop antennas connected to a network analyzer, which measures the amplitude and phase of the wave in two dimensions (r and z). In addition the frequency of the signals is also swept over a range of several hundreds of megahertz, providing a comprehensive picture of the near and far field antenna radiation patterns over a variety of plasma conditions. The magnetic field is varied from a few gauss to 200 G, with the density variable over at least 3 decades from 10 7 to 10 10 cm -3 . The waves are shown to lie on the dispersion surface for whistler waves, with observation of resonance cones in agreement with theoretical predictions. The waves are also observed to propagate without loss of amplitude at higher power, a result in agreement with previous experiments and the notion of ducted whistlers.

A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models

In recent years, the advance of the elliptical resonant cavity and focus cavity is known by many people. There are homogeneous and multipatternal virtues in the focus dimensional microwave field of the elliptical resonant cavity. It is very suitable for applying the low power microwave biological effect equipment. However, when designing the elliptical resonant cavity may meet the problems of complex and huge computation need to be solved. This paper proposed the simple way of approximate processing the Mathieu function. It can greatly simplify the difficulty and decrease the scale of computation. This method can satisfy the requirements of research and development within project permitted precision.

We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.

This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.

The polarization characteristics of the radiation from a quasi-steady pulsar magnetosphere are calculated using the amplitude-modulated-noise interpretation of the data on pulse structures. The total emission consists of three incoherently mixed radiation streams. Two of the independent polarization states are ellipticallypolarized (modes I and II) and one is linearly polarized (mode III). In the regime where the length scale of the radial distribution of the electric current density is appreciably longer than the wavelength of the radiation, the position angles of modes I and II are orthogonal and those of modes I and III coincident. However, the senses of circular polarization of modes I and II are in general uncorrelated. The degrees of circular polarization of the 'orthogonal' modes are decreasing functions of frequency and both approach zero in the limit where the frequency of the radiation is much higher than the rotation frequency of the pulsar. Longitudinal changes in the position angle and in the sense of circular polarization of each of the ellipticallypolarized modes are shown to arise, together with mode transitions, in part from the stochastic fluctuations and in part from the systematic variations of the electric current density with the azimuthal angle, in a narrow emitting region adjacent to the light cylinder. (author)

Some recent experiments involving polarized neutrons are discussed; they demonstrate how polarization studies provide information on fundamental aspects of nuclear structure that cannot be obtained from more traditional neutron studies. Until recently, neutron polarization studies tended to be limited either to very low energies or to restricted regions at higher energies, determined by the kinematics of favorable (p, vector n) and (d, vector n) reactions. With the advent of high intensity pulsed electron and proton accelerators and of beams of vector polarized deuterons, this is no longer the case. One has entered an era in which neutron polarization experiments are now being carried out, in a routine way, throughout the entire range from thermal energies to tens-of-MeV. The significance of neutron polarization studies is illustrated in discussions of a wide variety of experiments that include the measurement of T-invariance in the β-decay of polarized neutrons, a search for the effects of meson exchange currents in the photo-disintegration of the deuteron, the determination of quantum numbers of states in the fission of aligned 235 U and 237 Np induced by polarized neutrons, and the double- and triple-scattering of fast neutrons by light nuclei

We have theoretically studied the electronic and optical properties of a GaAs/AlGaAs elliptic quantum ring under in-plane electric field. The effects of an eccentric internal barrier -placed along the electric field direction, chosen as x-axis- and incident light polarization are particularly taken into account. The one-electron energy spectrum and wave functions are found using the adiabatic approximation and the finite element method within the effective-mass model. We show that it is possible to repair the structural distortion by applying an appropriate in-plane electric field, and the compensation is almost complete for all electronic states under study. For both concentric and eccentric quantum ring the intraband optical properties are very sensitive to the electric field and probe laser polarization. As expected, in the systems with eccentricity distortions the energy spectrum, as well as the optical response, strongly depends on the direction of the externally applied electric field, an effect that can be used as a signature of ring eccentricity. We demonstrated the possibility of generating second harmonic response at double resonance condition for incident light polarized along the x-axis if the electric field or/and eccentric barrier break the inversion symmetry. Also, strong third harmonic signal can be generated at triple resonance condition for a specific interval of electric field values when using y-polarized light.

The propagation of the first ionization wave in a compact fluorescent lamp (T4 tube with standard electrodes) during ignition was investigated for various initial dc-voltages (both polarities measured against ground) and gas compositions (with and without mercury). In addition the effect of the presence of a fluorescent powder coating was studied. The propagation velocity of the initial wave was measured by an assembly of photomultipliers installed along the tube, which detected the light emitted by the wave head. The propagation was found to be faster for positive than for negative polarity. This effect is explained involving processes in the electrode region as well as in the wave head. Waves propagate faster in the presence of a fluorescent powder coating than without it and gases of lighter mass show a faster propagation than gases with higher mass

In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly

Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be diffe...

Full Text Available Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential. [Projekat Ministarstva nauke Republike Srbije, br. 174020: Geometry and Topology of Manifolds and Integrable Dynamical Systems

Full Text Available The electron energy spectrum in core-shell elliptic quantum wire and elliptic semiconductor nanotubes are investigated within the effective mass approximation. The solution of Schrodinger equation based on the Mathieu functions is obtained in elliptic coordinates. The dependencies of the electron size quantization spectrum on the size and shape of the core-shell nanowire and nanotube are calculated. It is shown that the ellipticity of a quantum wire leads to break of degeneration of quasiparticle energy spectrum. The dependences of the energy of odd and even electron states on the ratio between semiaxes are of a nonmonotonous character. The anticrosing effects are observed at the dependencies of electron energy spectrum on the transversal size of the core-shell nanowire.

The Jacobian elliptic functions are applied to the motion of nonzero-rest-mass particles in the Schwarzschild geometry. The bound and unbound trajectories are analysed together with their classical and special-relativity limits.

Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

N-body simulations have been carried out in order to explore the final state of elliptical galaxies after encounters and more expecifically whether the Fundamental Plane (FP hereafter) relation is affected by merging.

National Aeronautics and Space Administration — It is proposed to develop and implement a simulation of spacecraft rendezvous and docking guidance, navigation, and control in elliptical orbit. The foundation of...

We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs

We propose a new approach that enables full control over the three-dimensional state of polarization and the field distribution near the focus of a high numerical aperture objective lens. By combining the electric dipole radiation and a vectorial diffraction method, the input field at the pupil plane for generating arbitrary three-dimensionally oriented linear polarization at the focal point with a diffraction limited spot size is found analytically by solving the inverse problem. Arbitrary three-dimensional ellipticalpolarization can be obtained by introducing a second electric dipole oriented in the orthogonal plane with appropriate amplitude and phase differences

… very comprehensive coverage of this vast subject area … a useful and essential treatise for anyone involved in elliptic curve algorithms … this book offers the opportunity to grasp the ECC technology with a diversified and comprehensive perspective. … This book will remain on my shelf for a long time and will land on my desk on many occasions, if only because the coverage of the issues common to factoring and discrete log cryptosystems is excellent.-IACR Book Reviews, June 2011… the book is designed for people who are working in the area and want to learn more about a specific issue. The chapters are written to be relatively independent so that readers can focus on the part of interest for them. Such readers will be grateful for the excellent index and extensive bibliography. … the handbook covers a wide range of topics and will be a valuable reference for researchers in curve-based cryptography. -Steven D. Galbraith, Mathematical Reviews, Issue 2007f.

Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution of hot and dense nuclear matter produced in non-central relativistic heavy-ion collisions is discussed. The elliptic flow parameter v{sub 2} is obtained by Fourier analysis of the azimuthal distribution of pions and protons which are emitted from the freeze-out hypersurface. As a function of rapidity, the pion and proton elliptic flow parameters both have a peak at midrapidity. (author)

Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves in terms of finite sums over canonical binary quadratic forms. This yields vastly simpler formulas related to work of Birch and Swinnerton-Dyer for such $L$-values, and extends beyond their framework to special non-CM elliptic curves.

the sideward flow, the elliptic flow and the radial transverse mass distribution of protons data at. AGS energies. In order to ... data on both sideward and elliptic flow, NL3 model is better at 2 A¡GeV, while NL23 model is at 4–8. A¡GeV. ... port approach RBUU which is based on a coupled set of covariant transport equations for.

By using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit, and extrinsic orbital angular-momentum and intrinsic orbital angular-momentum couplings induced by torsion, which can lead to geometric phase, spin, and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert a right-handed circularly polarized electromagnetic wave into a left-handed polarized one, vice versa. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.

Quartz crystal resonators (QCRs) with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin's theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

The space-time propagation of heavy quarks in ultrarelativistic heavy ion collisions is studied within the partonic transport model Boltzmann approach of multiparton scatterings (BAMPS). In this model heavy quarks interact with the partonic medium via binary scatterings. The cross sections for these interactions are calculated with leading-order perturbative QCD, but feature a more precise Debye screening derived within the hard thermal loop approximation and obey the running of the coupling. Within this framework the elliptic flow and the nuclear modification factor of heavy quarks are computed for the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) energies and compared to available experimental data. It is found that binary scatterings alone cannot reproduce the data and therefore radiative corrections have to be taken into account.

This paper presents a study of the self-focusing and self-defocusing of elliptically shaped Gaussian laser beams in collisional and collisionless plasmas. The non-linear dependence of the dielectric constant inside a collisional plasma is due to inhomogeneous heating of energy carriers and in a collisionless plasma it is due to the ponderomotive force. It is found that the beam gets focused at different points in different planes, exhibiting the effect of astigmatism. In certain power regions considered, the beam either converges or defocuses in both the directions, while in some other regions of the power spectrum one dimension of the beam focuses while the other defocuses. The beam also propagates in an oscillatory waveguide.

Produced partons have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage of non-central heavy-ion collisions. Parton scattering is shown to polarize quarks along the same direction due to spin-orbital coupling.Such global quark polarization will lead to many observable consequences,such as left-right asymmetry of hadron spectra, global transverse polarization of thermal photons, dileptons and hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow. Global hyperon polarization is predicted with indifferent hadronization scenarios and can be easily tested.

On the basis of the HADAS spectrometer in the guide hall of the Juelich research reactor FRJ-2 a polarized neutron reflectometer is build with a 2D-position sensitive detector system. The new spectrometer is optimized for reflectivity and diffuse magnetic scattering measurements with small incident angles on thin magnetic films with thicknesses in the nm range. The polarization analyzer covers the whole detector area, so that a range of 2.5 deg in the scattering angle can be measured simultaneously. The analyzer consists of a stack of supermirrors tilted against the scattering plane. In this reflection geometry, the momentum transfer resolution of the instrument is not reduced, but the sample height is limited to 17 mm. For the monochromator, polarizer and collimation different setups have been compared on the basis of Monte-Carlo calculations: a focusing elliptical supermirror monochromator, a cylindrical mirror, a focusing pyrolytic graphite double monochromator and a double monochromator with bent perfect Si crystals. (author)

The degree of polarization (DOP) can be used to characterize the polarization-maintaining ability of a beam of polarized light propagating through a turbid medium. Experiments on polystyrene (PST) sphere suspensions show that, the linearly polarized light propagating through the PST sphere suspension of Rayleigh scatterers has better polarization-maintaining ability, whereas the circularly polarized light propagating through the PST sphere suspension of Mie scatterers has better polarization-maintaining ability. Moreover, helicity flipping occurs to the circularly polarized light propagating in the extremely weak PST sphere suspensions or on the surface of suspensions. In addition, the DOP is dependent on the wavelength of incident light. The results can be helpful to image in turbid media by use of diffuse backscattered light. (paper)

A cup waveguide antenna with integrated polarizer and OMT for simultaneously communicating left and right hand circularly polarized electromagnetic waves is adjustable to obtain efficient propagation and reception of electromagnetic waves. The antenna includes a circular waveguide having an orthomode transducer utilizing first and second pins longitudinally spaced apart and oriented orthogonally with respect to each other. Six radially-oriented adjustable polarizer screws extend from the exterior to the interior of the waveguide. A septum intermediate the first and second pins is aligned with the first pin. Adjustment of the polarizer screws enables maximized propagation of and/or response to left hand circularly polarized electromagnetic waves by the first pin while simultaneously enabling maximized propagation of and/or response to right hand circularly polarized electromagnetic waves by the second pin.

Ferroelectricity occurs in many different kinds of materials. Many of the technologically important solids, which are ferroelectric, can be classified as ionic. Any microscopic theory of ferroelectricity must contain a description of local polarization forces. We have collaborated in the development of a theory of ionic polarization which is quite successful. Its basic assumption is that the polarization is derived from the properties of the individual ions. We have applied this theory successfully to diverse subjects as linear and nonlinear optical response, phonon dispersion, and piezoelectricity. We have developed numerical methods using the local Density approximation to calculate the multipole polarizabilities of ions when subject to various fields. We have also developed methods of calculating the nonlinear hyperpolarizability, and showed that it can be used to explain light scattering experiments. This paper elaborates on this polarization theory

We study the linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma. The drift mode excited in such a plasma is dispersive in nature. The drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. To study the effect of the nonlinear coupling on the propagation of energy in a collision free plasma, we solve the Hasegawa-Mima equation as a mixed initial boundary-value problem. The solutions of the linearized equation are used to check the reliability of our numerical calculations. Additional checks are also performed on the invariants of the system. Our results reveal that a pulse gets distorted as it propagates through the medium. The peak of the pulse propagates with a finite velocity that depends on the amplitude of the initial pulse. The polarity of propagation depends on the initial parameters of the pulse. We have also studied drift wave propagation in a resistive plasma. The Hasegawa-Wakatani equations are used to investigate this problem

associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving

This report describes the theoretical calculations related with the electron cyclotron (EC) waves polarization control in the TJII stellarator. Two main aspects will be distinguished: the determination of the vacuum polarization that the wave must exhibit if a given propagation mode in a cold plasma is desired and the calculation of the behavior of the grooved polarizers and other transmission systems used to launch the vacuum wave with the required polarization. (Author) 13 refs.

In a theoretical review of polarization experiments two important points are emphasized: (a) their versatility and their relevance to a large variety of aspects of hadron physics (tests of basic symmetries; a probe of strong interaction dynamics; a tool for hadron spectroscopy); (b) the wealth of experimental data on polarization parameters in pp and np scattering in the Regge language and in the diffraction language. (author)

The anisotropic effects of random density irregularities in causing Faraday polarization fluctuations of VHF radio signals are examined, taking both rod-like and sheet-like irregularities into consideration. It is found that the variance of Faraday polarization fluctuations depends on the ratio of perpendicular to parallel correlation lengths. The anisotropic effect of rod-like ionospheric irregularities are shown to be most appreciable for longitudinal propagation. The anisotropic effect of sheet-like ionospheric irregularities, however, is not strongly dependent on the radio propagation angle. During transionospheric propagation at large angles with respect to the geomagnetic field, sheet-like irregularities may cause greater Faraday polarization fluctuations than rod-like irregularities.

The authors present an introduction to internal polarized gaseous targets, polarization method, polarization measurement method and procedure. To get the total nuclear polarization of hydrogen atoms (including the polarization of the recombined hydrogen molecules) in the target cell, authors have measured the parameters relating to atomic polarization and polarized hydrogen atoms and molecules. The total polarization of the target during our measurement is P T =0.853 ± 0.036. (authors)

Propagation characteristics of hydromagnetic waves in a magnetic plasma are investigated using the two-plasma fluid equations including the effect of lower-hybrid waves propagating perpendicularly to the magnetic field. The effect of lower-hybrid waves on the propagation of hydromagnetic waves is analysed in terms of phase speed, growth rate, refractive index, polarization and the amplitude relation between the density perturbation and the magnetic-field perturbation for the cases when hydromagnetic waves propagate in the plane whose normal is perpendicular to both the magnetic field and the propagation direction of lower-hybrid waves and in the plane perpendicular to the propagation direction of lower-hybrid waves. It is shown that hydromagnetic waves propagating at small angles to the propagation direction of lower-hybrid waves can be excited by the effect of lower-hybrid waves and the energy of excited waves propagates nearly parallel to the propagation direction of lower-hybrid waves. (author)

We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)

Various sources of polarized neutrons are reviewed. Monoenergetic source produced with unpolarized or polarized beams, white sources of polarized neutrons, production by transmissions through polarized hydrogen targets and polarized thermal neutronsare discussed, with appropriate applications included. (U.K.)

Recent research work on speckle patterns indicates a variation of the polarization state during propagation and its nonuniformly spatial distribution. The preliminary step for the investigation of this polarization speckle is the generation of the corresponding field. In this paper, a kind...... of special depolarizer: the random roughness birefringent screen (RRBS) is introduced to meet this requirement. The statistical properties of the field generated by the depolarizer is investigated and illustrated in terms of the 2x2 beam coherence and polarization matrix (BCPM) with the corresponding degree...... of coherence (DoC). and degree of polarization (DoP) P. The changes of the coherence and polarization when the speckle field propagates through any optical system are analysed within the framework of the complex ABCD-matrix theory....

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...

In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.

Consequences of the thermal microwave burst model proposed earlier have been considered. According to the model the centimeter burst is generated at the heat propagation to the upper atmosphere. The polarization features of the burst are explained: a change of the polarization sign in a frequency range, a rapid change of the polarization sign in the development of a burst at a fixed frequency, a lack of time coincidence of the moments of the burst maximum of the polarization and of the total flux. From the model the consequences are obtained, which are still not confirmed by experiment. An ordinary-type wave prevails in the burst radiation, in the course of which the polarization degree falls on the ascending branch of bursts development. At the change of the polarization sign at the fixed frequency prior to the sign change an ordinary-type wave should be present in excess and later an extreordinary type wave.

Scaling of the Landau gauge gluon propagator calculated at {beta} = 6.0 and at {beta} = 6.2 is demonstrated. A variety of functional forms for the gluon propagator calculated on a large (32{sup 3} x 64) lattice at {beta} = 6.0 are investigated.

A new engineering model for sound propagation in cities is presented. The model is based on numerical and experimental studies of sound propagation between street canyons. Multiple reflections in the source canyon and the receiver canyon are taken into account in an efficient way, while weak

Free-space light can be coupled into propagating surface waves at a metal–dielectric interface, known as surface plasmons (SPs). This process has traditionally faced challenges in preserving the incident polarization information and controlling

In high energy heavy ion collisions and interacting cold atom systems, large elliptic flow anisotropies have been observed. For the large opacity (ρ σ L ˜103 ) of the latter hydrodynamics is a natural consequence, but for the small opacity (ρ σ L ˜1 ) of the former the hydrodynamic description is questionable. To shed light onto the situation, we simulate the expansion of a low density argon ion (or atom) system, initially trapped in an elliptical region, under the Coulomb interaction (or elastic scattering). Significant elliptic anisotropy is found in both cases, and the anisotropy depends on the initial spatial eccentricity and the density of the system. The results may provide insights into the physics of anisotropic flow in high energy heavy ion collisions and its role in the study of quantum chromodynamics.

Chemical evolution models for the Galaxy and ellipticals, which take into account the most recent developments on theories of nucleosynthesis and supernova progenitors, are presented. The evolution of the abundance of iron in these systems, under the assumption that this element is mainly produced by type I SNe, originating from white dwarfs in binary systems, has been computed and the results have been compared with the observations. Overabundances of O, Si, Ne and Mg with respect to iron have been predicted for halo stars in their Galaxy. The existence of an Fe - total mass relation with a slope steeper than the corresponding relations for Mg and O has been predicted for ellipticals. The masses of Fe ejected by ellipticals of various masses into the intergalactic medium have also been computed in detail. The general agreement obtained between these theoretical models and the observations for galaxies of different morphological type supports the assumptions made about the origin of iron

Full Text Available According to the general theory of relativiy, a black hole is defined as a region of spacetime with super-strong gravitational effects and there is nothing can escape from it. So in the classical theory of relativity, it is safe to say that black hole is a "dead" thermodynamical object. However, by using quantum mechanics theory, Hawking has shown that a black hole may emit particles. In this paper, calculation of temperature of an elliptical black hole when emitting the Dirac particles was presented. By using the complexpath method, radiation can be described as emission process in the tunneling pictures. According to relationship between probability of outgoing particle with the spectrum of black body radiation for fermion particles, temperature of the elliptical black hole can be obtained and it depend on the azimuthal angle. This result also showed that condition on the surface of elliptical black hole is not in thermal equilibrium.

This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the...

This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.

Brief review is presented of the high energy polarization study including experimental data and the theoretical descriptions. The mostimportant proposals at the biggest accelerators and the crucial technical developments are also listed which may become a main-line of spin physics. 35 refs.; 10 figs.; 4 tabs

These three images were taken on three different orbits over the north polar cap in April 1999. Each shows a different part of the same ice-free trough. The left and right images are separated by a distance of more than 100 kilometers (62 miles). Note the similar layers in each image.

Although polarizers and detectors take an important part in discussions and experimental tests about E.P.R. paradox, they are not explicitly present in usual calculations. A calculation is presented using propagators of the correlation in linear polarization of two photons emitted in a 0→1→0 atomic cascade, by quantum field theory, for a diagram including two polarized atoms taking place of polarizers and detectors. (author)

In order to determine transfer coefficients for plate fin and elliptical tube exchangers, mass transfer experiments have been performed using the naphthalene sublimation technique. By means of the heat-mass transfer analogy, the results can be converted to heat transfer results. The transfer coefficients were compared with those for circular tube exchangers and the comparison revealed no major differences. This is a positive outcome, since the use of elliptical tubes may reduce substantially the pressure drop, without affecting the transfer characteristics.(Author) [pt

We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirr...

Full Text Available A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.

This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross-diffusion......This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross...

Full Text Available We show quantitatively whether giant elliptical galaxies would be visible at far UV wavelengths if they were placed at moderate redshift of 0.4-0.5. On the basis of simple cosmological tests, we conclude that giant elliptical galaxies can be detectable upto the redshift of 0.4-0.5 in the proposed GALEX (Galaxy Evolution Explorer Deep Imaging Survey. We also show that obtaining UV color index such as m_1550 - V from upcoming GALEX and SDSS (Sloan Digital Sky Survey observations should be feasible.

Using fast-camera measurements the generation mechanism of plasma blobs is investigated in the linear device CSDX. During the ejection of plasma blobs the plasma is dominated by an m=1 mode, which is a counterrotating vortex pair. These flows are known to be subject to the cooperative elliptic instability, which is characterized by a cooperative disturbance of the vortex cores and results in a three-dimensional breakdown of two-dimensional flows. The first experimental evidence of a cooperative elliptic instability preceding the blob-ejection is provided in terms of the qualitative evolution of the vortex geometries and internal wave patterns.

A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top of the infla......A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top...

According to one of Maldacena's dualities, type IIB string theory on AdS 3 x S 3 x K3 is equivalent to a certain N = (4, 4) superconformal field theory. In this note we compute the elliptic genus of the boundary theory in the supergravity approximation. A finite quantity is obtained once we introduce a particular exclusion principle. In the regime where the supergravity approximation is reliable, we find exact agreement with the elliptic genus of a sigma model with target space K3 N /S N

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

The lectures as delivered contained an elementary introduction to the classical theory of black holes together with an account of Hawking's original derivation of the thermal emission from black holes in the quantum theory. Also described here is what is here called the elliptic interpretation partly because of its possible relevance to the lectures of Professor 't Hooft. A rather more detailed account of the elliptic interpretation is given and the reader is referred to the original literature for the elementary material. 22 references

In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \\times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.

Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in (Au+Au) collisions at sqrt {sNN}=200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.

Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.

In order to check the ability of the simplified assessment procedure (A16 guide) to predict fatigue crack growth, a benchmark problem was conducted. This work is carried out under the project ''agreement on the Exchange of Information and Collaboration in the field of Research and Development of Fast Breeder Reactor (FBR) between Europe (EU) and Japan''. Experimental work is conducted by PNC using Air cooled Thermal transient Test Facility (ATTF). Specimen is a thick wall tube containing a semi elliptical (3-D) circumferential crack and subjected to cyclic thermal transients. The constitutive material is the 304 austenitic stainless steel type SUS304. Due to thermal shock (650 C-300 C) the stress distribution through the wall is non-linear and well approximated using a 3 rd order polynomial. When comparing computations and tests data we observe a good agreement for the crack propagation in length. In crack depth, accurate results are obtained in the first part of the test, but on the later stage of the experiment the computations slightly underestimate the propagation (deep crack). In addition, we notice the importance of good evaluation of fracture mechanics parameters for non-linear stress distribution through the wall. At present A16 guide handbook gives stress intensity factor solutions for non-linear stress distribution through the wall. (author)

Advances in the general theory of wave propagation in layered viscoelastic media reveal new insights regarding seismic waves in the Earth. For example, the theory predicts: 1) P and S waves are predominantly inhomogeneous in a layered anelastic Earth with seismic travel times, particle-motion orbits, energy speeds, Q, and amplitude characteristics that vary with angle of incidence and hence, travel path through the layers, 2) two types of shear waves exist, one with linear and the other with elliptical particle motions each with different absorption coefficients, and 3) surface waves with amplitude and particle motion characteristics not predicted by elasticity, such as Rayleigh-Type waves with tilted elliptical particle motion orbits and Love-Type waves with superimposed sinusoidal amplitude dependencies that decay exponentially with depth. The general theory provides closed-form analytic solutions for body waves, reflection-refraction problems, response of multiple layers, and surface wave problems valid for any material with a viscoelastic response, including the infinite number of models, derivable from various configurations of springs and dashpots, such as elastic, Voight, Maxwell, and Standard Linear. The theory provides solutions independent of the amount of intrinsic absorption and explicit analytic expressions for physical characteristics of body waves in low-loss media such as the deep Earth. The results explain laboratory and seismic observations, such as travel-time and wide-angle reflection amplitude anomalies, not explained by elasticity or one dimensional Q models. They have important implications for some forward modeling and inverse problems. Theoretical advances and corresponding numerical results as recently compiled (Borcherdt, 2008, Viscoelastic Waves in Layered Media, Cambridge University Press) will be reviewed.

We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak-lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between ℓ ≃ 40 and ℓ ≃ 400 before that of spiral galaxies dominates on higher multipoles. The predominant term on intermediate scales is the negative cross-correlation between intrinsic alignments and weak gravitational lensing (GI-alignment). We simulate parameter inference from weak gravitational lensing with intrinsic alignments unaccounted; the bias induced by ignoring intrinsic alignments in a survey like Euclid is shown to be several times larger than the statistical error and can lead to faulty conclusions when comparing to other observations. The biases generally point into different directions in parameter space, such that in some cases one can observe a partial cancellation effect. Furthermore, it is shown that the biases increase with the number of tomographic bins used for the parameter estimation process. We quantify this parameter estimation bias in units of the statistical error and compute the loss of Bayesian evidence for a model due to the presence of systematic errors as well as the Kullback-Leibler divergence to quantify the distance between the true model and the wrongly inferred one.

Polarization involves the vectorial nature of light fields. In current applications of optical science, the electromagnetic description of light with its vector features has been shown to be essential: In practice, optical radiation also exhibits randomness and spatial non-uniformity of the polarization state. Moreover, propagation through photonic devices can alter the correlation properties of the light field, resulting in changes in polarization. All these vectorial properties have been gaining importance in recent years, and they are attracting increasing attention in the literature. This is the framework and the scope of the present book, which includes the authors’ own contributions to these issues.

In this work, we present the design study of an elliptical solenoid magnet to be used for transverse beam matching at the input of a spiral inflector for efficient transmission. We have studied the dependence of axial field and gradients in the transverse directions of the elliptical solenoid magnet with ellipticity of the aperture. Using the beam envelope equations we have studied the feasibility of using an elliptical solenoid for transverse beam matching to the acceptance of a spiral inflector. (author)

A propagation researcher or a systems engineer who intends to use the results of a propagation experiment is generally faced with various database tasks such as the selection of the computer software, the hardware, and the writing of the programs to pass the data through the models of interest. This task is repeated every time a new experiment is conducted or the same experiment is carried out at a different location generating different data. Thus the users of this data have to spend a considerable portion of their time learning how to implement the computer hardware and the software towards the desired end. This situation may be facilitated considerably if an easily accessible propagation database is created that has all the accepted (standardized) propagation phenomena models approved by the propagation research community. Also, the handling of data will become easier for the user. Such a database construction can only stimulate the growth of the propagation research it if is available to all the researchers, so that the results of the experiment conducted by one researcher can be examined independently by another, without different hardware and software being used. The database may be made flexible so that the researchers need not be confined only to the contents of the database. Another way in which the database may help the researchers is by the fact that they will not have to document the software and hardware tools used in their research since the propagation research community will know the database already. The following sections show a possible database construction, as well as properties of the database for the propagation research.

In the last decade the performance of neutron guides for the transport of neutrons has been significantly increased. The most recent developments have shown that elliptic guide systems can be used to focus neutron beams while simultaneously reducing the number of neutron reflections, hence, leading to considerable gains in neutron flux. We have carried out Monte-Carlo simulations for a new triple-axis spectrometer that will be built at the end position of the conventional cold guide NL-1 in the neutron guide hall of the research reactor FRM-II in Munich, Germany. Our results demonstrate that an elliptic guide section at the end of a conventional guide can be used to at least maintain the total neutron flux onto the sample, while significantly improving the energy resolution of the spectrometer. The simulation further allows detailed insight how the defining parameters of an elliptic guide have to be chosen to obtain optimum results. Finally, we show that the elliptic guide limits losses in the neutron flux that generally arise at the gaps, where the monochromator system of the upstream instrument is situated.

The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r b , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.

textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is

Mar 21, 2018 ... One of the key a priori estimates in the theory of second-order elliptic .... It is well known that the maximal functions satisfy strong p–p .... Here we prove the following auxiliary result, which will be a crucial ingredient in the proof.

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

elliptical crack in a thick-walled cylinder subjected to transient dynamic stresses. First, the problem of dynamic elasticity in a thick-walled cylinder is solved analytically using the finite Hankel transform. Transient pressure is assumed to act on ...

result in a breakdown of the geometrical focusing mechanism inherent to the elliptical shape, resulting in unwanted reflections and loss of transmission. We present a new and yet untried idea by curving a guide in such a way as to follow the ballistic curve of a neutron in the gravitational field, while...

Galleas, W., E-mail: w.galleas@uu.nl [ARC Centre of Excellence for the Mathematics and Statistics of Complex Systems, University of Melbourne, VIC 3010 (Australia)

2013-02-21

In this work we refine the method presented in Galleas (2012) [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation arises from the dynamical Yang-Baxter relation and its solution is given in terms of multiple contour integrals.

The study investigates the laminar flow and heat transfer characteristics in elliptic micro-channels of varying axis ratios and with internal longitudinal fins, operating in a region that is hydrodynamically and thermally fully developed; purposely to determine the effects of some salient fluid and geometry parameters such as ...

We discuss hadron production in relativistic heavy-ion collisions in the framework of the recombination and fragmentation model. We propose elliptic flow as a useful tool for exploring final interactions of resonances, the hadron structure of exotic particles and the phase structure of the reaction.

The effect of the ellipticity of the plasma cross section on tearing mode stability is investigated. The induced coupling between modes is shown to be destabilizing; however, the modification of the equilibrium tends to stabilize the tearing modes. The net effect depends on the manner in which the equilibrium is modified as the plasma cross-section shape is changed

Based on the number of 'new' comets seen on near-parabolic orbits, one can predict the number of comets that should be found on definitely elliptical orbits on their subsequent returns. The author shows that about three out of four of these returning comets are not observed. (Auth.)

The aim of this paper is to investigate the existence of solutions of a nonlocal semi linear elliptic equation with an indefinite term. The monotone method, the method of upper and lower solutions and the classical maximum principle are used to obtain our results. (author)

This paper presents a scalable hardware implementation of both commonly used public key cryptosystems, RSA and Elliptic Curve Cryptosystem (ECC) on the same platform. The introduced hardware accelerator features a design which can be varied from very small (less than 20 Kgates) targeting wireless

In this paper we evaluate the difference between the inverse operators of a Dirichlet problem and of a diffraction problem for parameter-elliptic convolution operators with constant symbols. We prove that the inverse operator of a Dirichlet problem can be obtained as a limit case of such a diffraction problem. Quaestiones ...

This paper is the first to investigate the power of the Cell Broadband Engine for state-of-the-art public-key cryptography. We present a high-speed implementation of elliptic-curve Diffie-Hellman (ECDH) key exchange for this processor, which needs 697080 cycles on one Synergistic Processor Unit for

In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.

Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.

Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.

Full Text Available In this article, we prove the existence and the regularity of distributional solutions for a class of nonlinear anisotropic elliptic equations with $p_i(x$ growth conditions, degenerate coercivity and $L^{m(\\cdot}$ data, with $m(\\cdot$ being small, in appropriate Lebesgue-Sobolev spaces with variable exponents. The obtained results extend some existing ones [8,10].

A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. Let a and b be complex numbers such that a and b are not among the poles of p. A lower bound is given for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers, expressed in their heights and degrees. By

Mean transfer coefficients in elliptical tubes and plate fin heat exchangers were determined by application of heat and mass transfer analogy in conjunction with the naphthalene sublimation technique. The transfer coefficients are presented in a dimensionless form as functions of the Reynolds number. By using the least squares method analytical expressions for the transfer coefficients were determined with low scattering. (E.G.) [pt

In this work we refine the method presented in Galleas (2012) [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation arises from the dynamical Yang–Baxter relation and its solution is given in terms of multiple contour integrals.

Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from SL(3, Z)-modular transformation properties of the kernels of dual indices.

Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$

The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

10Ne20+13Al27, 18Ar40+21Sc45, 30Zn64+28Ni58, 36Kr86+41Nb93) using the quantum molecular dynamics (QMD) model. General features of elliptic ﬂow are investigated with the help of theoretical simulations. The simulations are ...

Accurate surface photometry has been obtained in J and K for 12 giant elliptical galaxies. Ellipses have been fitted, to obtain luminosity, ellipticity, and major axis position angle profiles. The results have been combined with visual profiles from CCD observations. It is found that elliptical

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

A small number of low-luminosity elliptical galaxies in the Virgo cluster and around other prominent galaxies have been studied using photoelectric and photographic techniques. The color-magnitude relation for ellipticals now extends from M/sub v/ = -23 to -15, and is linear over that range with a slope of 0.10 in U-V per visual magnitude. Galaxies which are known to contain a large number of young stars (''extreme cases'') are from 0.10 to 0.20 mag bluer in U-V than the lower envelope of the dwarf elliptical color-magnitude relation. This difference can be accounted for if the dwarf elliptical galaxies are young, but do not contain the massive blue stars that probably exist in the young populations of the extreme cases. Surface brightness profiles of the dwarfs have revealed some interesting distinctions between themselves and the brighter E's. In general, their intensity profiles are shallower than those of the bright E's, meaning they are of lower mean density. These mean densities are also a function of the total luminosity. Unlike the bright E's, the surface brightnesses near the centers are also a strong function of the total luminosity. The presence of a nucleation, which can be as much as 2 mag brighter than what the outer envelope would predict, does not appear to depend on any other measurable property of the galaxies. The variation in surface brightness profiles at the same total luminosity is suggestive that the low-luminosity dwarfs formed in more than one way. The flattening distribution of the dwarfs is like that of the bright ellipticals, and is also similar to the flattening distribution of field irregular galaxies

Full Text Available A small size elliptically tapered slot antenna (ETSA fed by coplanar waveguide (CPW for ultra-wideband (UWB applications is proposed. It is printed on an FR4 substrate and occupies a size of 37×34×0.8 mm^3. A pair of quarter circular shapes is etched on the radiator to reduce the size. To overcome the limitation of uniform corrugation, non-uniform corrugation is utilized to reduce the cross-polarization level. A parametric study is carried out to investigate the effects of circular cut and corrugations. In order to validate the design, a prototype is fabricated and measured. Both simulated and measured results confirm that the proposed antenna achieves a good performance of a reflection coefficient below -10 dB from 3.1 GHz to 10.6 GHz, including a maximum antenna gain of 8.1dBi, directional patterns in the end-fire direction, low cross-polarization level below -20 dB and linear phase response. The antenna is promising for applications in UWB impulse radar imaging.

Circularly polarized light can be divided into two vertically linearly polarized light beams with ±π/2 phase differences. In the presence of an external magnetic field, when circularly polarized light travels through a ferrofluid film, whose thickness is no more than that of λ/4 plate, magneto-optical, magnetic birefringence and dichroism effects cause the transmitted light to behave as ellipticallypolarized light. Using angular scan by a continuously rotating polarizer as analyzer, the angular (θ) distribution curve of relative intensity (T) corresponding to ellipticallypolarized light can be measured. From the T ‑ θ curve having ellipsometry, the parameters such as the ratio of short to long axis, and angular orientation of the long axis to the vertical field direction can be obtained. Thus, magnetic birefringence and dichroism can be probed simultaneously by measuring magneto-optical, positive or negative birefringence and dichroism features from the transmission mode. The proposed method is called θ-scan technique, and can accurately determine sample stability, magnetic field direction, and cancel intrinsic light source ellipticity. This study may be helpful to further research done to ferrofluids and other similar colloidal samples with anisotropic optics.

A correction term is introduced in the stationary-point analysis on high-order harmonic generation (HHG) from aligned molecules. Arising from a multi-centre expansion of the electron wave function, this term brings our numerical calculations of the Lewenstein model into qualitative agreement...

metamaterial can remain flat and is above 0.7 within a broad band. Moreover, the metamaterial can be designed as a broadband quarter wave plate. A sample metamaterial was fabricated and tested to prove the validity of the simulations, and the sample could work

The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and corotating with the pulsar magnetosphere. Within the 1/γ emission cone, the waves can be divided into two natural wave-mode components, the ordinary (O) mode and the extraordinary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the corotation of relativistic particles with magnetosphere is not considered, the intensity distributions for the X-mode and O-mode components are quite similar within the pulsar beam, which causes serious depolarization. However, if the corotation of relativistic particles is considered, the intensity distributions of the two modes are very different, and the net polarization of outcoming emission should be significant. Our numerical results are compared with observations, and can naturally explain the orthogonal polarization modes of some pulsars. Strong linear polarizations of some parts of pulsar profile can be reproduced by curvature radiation and subsequent propagation effect.

18 August 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows dark-outlined polygons on a frost-covered surface in the south polar region of Mars. In summer, this surface would not be bright and the polygons would not have dark outlines--these are a product of the presence of seasonal frost. Location near: 77.2oS, 204.8oW Image width: width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Spring

New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sérsic log I vprop r 1/n functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes MVT 4 uncorrelated with MVT . They also are α-element enhanced, implying short star-formation timescales. And their stellar populations have a variety of ages but mostly are very old. Extra light ellipticals generally rotate rapidly, are more isotropic than core Es, and have disky isophotes. We show that they have n sime 3 ± 1 almost uncorrelated with MVT and younger and less α-enhanced stellar populations. These are new clues to galaxy formation. We suggest that extra light ellipticals got their low Sérsic indices by forming in relatively few binary mergers, whereas giant ellipticals have n > 4 because they formed in larger numbers of mergers of more galaxies at once plus later heating during hierarchical clustering. We confirm that core Es contain X-ray-emitting gas whereas extra light Es generally do not. This leads us to suggest why the E-E dichotomy arose. If energy feedback from active galactic nuclei (AGNs) requires a "working surface" of hot gas, then this is present in core galaxies but absent in extra light galaxies. We suggest that AGN energy feedback is a strong function of galaxy mass: it is weak enough in small Es not to prevent merger starbursts but strong enough in giant Es and their progenitors to make dry mergers dry and to protect old stellar populations from late star formation. Finally, we verify that there is a strong

1. INTRODUCTION A medium’s susceptibility, hence the refractive index, the polarizability and the...frequencies. (3) Molecular polarizability is also frequency dependent. Electronic polarizability is present in all molecules and has a response time...representation: � . Trajectories on the Poincaré sphere the Krypton laser at λ = 647 nm, and the Argon laser at λ = (1) 457; (2) 476; and (3) 488

A critical challenge in the observation of the redshifted 21 cm line is its separation from bright Galactic and extragalactic foregrounds. In particular, the instrumental leakage of polarized foregrounds, which undergo significant Faraday rotation as they propagate through the interstellar medium, may harmfully contaminate the 21 cm power spectrum. We develop a formalism to describe the leakage due to instrumental widefield effects in visibility-based power spectra measured with redundant arrays, extending the delay-spectrum approach presented in Parsons et al. We construct polarized sky models and propagate them through the instrument model to simulate realistic full-sky observations with the Precision Array to Probe the Epoch of Reionization. We find that the leakage due to a population of polarized point sources is expected to be higher than diffuse Galactic polarization at any k mode for a 30 m reference baseline. For the same reference baseline, a foreground-free window at k > 0.3 h Mpc{sup −1} can be defined in terms of leakage from diffuse Galactic polarization even under the most pessimistic assumptions. If measurements of polarized foreground power spectra or a model of polarized foregrounds are given, our method is able to predict the polarization leakage in actual 21 cm observations, potentially enabling its statistical subtraction from the measured 21 cm power spectrum.

The propagation of submillimeter-waves (smm) in tokamak plasmas has been investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses have been carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system has been employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes have been developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements

Propagation of submillimeter waves (smm) in tokamak plasma was investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses were carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system was employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes were developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements. 5 references, 2 figures

Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component P z , the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of P z increases, the polarization response of the second-harmonic signal will vary from linear polarization to ellipticalpolarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral

In joint decision making, similarly minded people may take opposite positions. Consider the example of a marriage in which one spouse gives generously to charity while the other donates nothing. Such "polarization" may misrepresent what is, in actuality, a small discrepancy in preferences. It may be that the donating spouse would like to see 10% of their combined income go to charity each year, while the apparently frugal spouse would like to see 8% donated. A simple game-theoretic analysis suggests that the spouses will end up donating 10% and 0%, respectively. By generalizing this argument to a larger class of games, we provide strategic justification for polarization in many situations such as debates, shared living accommodations, and disciplining children. In some of these examples, an arbitrarily small disagreement in preferences leads to an arbitrarily large loss in utility for all participants. Such small disagreements may also destabilize what, from game-theoretic point of view, is a very stable equilibrium. Copyright 2001 Academic Press.

Propagation of Waves focuses on the wave propagation around the earth, which is influenced by its curvature, surface irregularities, and by passage through atmospheric layers that may be refracting, absorbing, or ionized. This book begins by outlining the behavior of waves in the various media and at their interfaces, which simplifies the basic phenomena, such as absorption, refraction, reflection, and interference. Applications to the case of the terrestrial sphere are also discussed as a natural generalization. Following the deliberation on the diffraction of the "ground? wave around the ear

It has been recntly shown that polarization state of propagation beam would suffer from polarization fluctuations due to the detrimental effects of atmospheric turbulence. This paper studies the performance of wireless optical communication (WOC) systems in the presence of polarization effect of atmosphere. We categorize the atmospheric polarization effect into polarization rotation, polarization-dependent power loss, and phase shift effect, with each effect described and modeled with the help of polarization-coherence theory and the extended Huygens-Fresnelprinciple. The channel matrices are derived to measure the cross-polarization interference of the system. Signal-to-noise ratio and bit error rate for polarization multiplexing system and polarization modulation system are obtained to assess the viability using the approach of M turbulence model. Monte Carlo simulation results show the performance of polarization based WOC systems to be degraded by atmospheric polarization effect, which could be evaluated precisely using the proposed model with given turbulent strengths.

As important components integrated in transmission lines of electron cyclotron heating systems, polarizers are mainly used to obtain the desired polarization for highly efficient coupling between electron cyclotron waves and plasma. The polarization strategy for 105-GHz electron cyclotron heating systems of HL-2M tokamak is studied in this paper. Considering the polarizers need high efficiency, stability, and low loss to realize any polarization states, two sinusoidal-grooved polarizers, which include a linear polarizer and an ellipticalpolarizer, are designed with the coordinate transformation method. The parameters, the period p and the depth d, of two sinusoidal-grooved polarizers are optimized by a phase difference analysis method to achieve an almost arbitrary polarization. Finally, the optimized polarizers are manufactured and their polarization characteristics are tested with a low-power test platform. The experimental results agree well with the numerical calculations, indicating that the designed polarizers can meet the polarization requirements of the electron cyclotron heating systems of HL-2M tokamak.

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future.

We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of R^4 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T^2, which we calculate explicitly.

An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.

We report the separation of the magnetization dynamics of densely packed nanomagnets depending on their orientation. The arrays consist of interleaved sublattices of identical nickel elliptical disks. By controlling the orientation of the elliptic disks relative to the external field in each sublattice, we simultaneously analyzed the magnetization dynamics in each sublattice using a time-resolved magnetooptic Kerr effect (TR-MOKE) microscopy system. The Fourier spectra showed clearly separated precession modes for sublattices with different orientations. The spectra were shown to be robust against the error in applied field orientation. The sublattice response can be tuned to a single collective frequency by choosing a symmetric field orientation. We analyzed the effect of the interelement coupling with various spacing between nanomagnets and found a relatively weak dependence on dipolar interactions in good agreement with micromagnetic simulations.

Gravitational radiation is a fundamental prediction of General Relativity. Elliptically deformed pulsars are among the possible sources emitting gravitational waves (GWs) with a strain-amplitude dependent upon the star's quadrupole moment, rotational frequency, and distance from the detector. We show that the gravitational wave strain amplitude h 0 depends strongly on the equation of state of neutron-rich stellar matter. Applying an equation of state with symmetry energy constrained by recent nuclear laboratory data, we set an upper limit on the strain-amplitude of GWs produced by elliptically deformed pulsars. Depending on details of the EOS, for several millisecond pulsars at distances 0.18 kpc to 0.35 kpc from Earth, the maximalh 0 is found to be in the range of ∼[0.4-1.5]x10 -24 . This prediction serves as the first direct nuclear constraint on the gravitational radiation. Its implications are discussed

Nonlinear finite element analyses of semi-elliptical surface cracks are performed under the fully plastic condition. The power-law hardening materials and the deformation theory of plasticity are assumed. Either the penalty function method or the Uzawa's algorithm is utilized to treat the incompressibility of plastic strains. The local and global J-integral values are obtained using a virtual crack extension technique for plates and cylinders with semi-elliptical surface cracks subjected to uniform tensions. The fully plastic solutions for surface cracked plates are given in the form of polynominals with geometric parameters a/t, a/c and the strain hardening exponent (n). In addition, the effects of curvature on fully plastic solutions are discussed through the comparison between the results of plates and cylinders. (author)

The multiplexing transmission has always been a focus of attention for communication technology. In this paper, the radiation characteristics of circular microstrip patch antenna was firstly analyzed based on cavity model theory, and then spiral beams carrying orbital angular momentum (OAM) were generated, using elliptical microstrip patch antenna, with a single feed probe instead of a standard circular patch with two feedpoints. Moreover, by combining the proposed elliptic microstrip patch antenna with Universal Software Radio Peripheral (USRP), a wireless OAM transmission system was established and the real-time transmission of text, image and video in a real channel environment was realized. Since the wireless OAM transmission has the advantage of good safety and high spectrum utilization efficiency, this work has theoretical significance and potential application.

Full Text Available A theoretical model of semi-elliptic surface crack growth based on the low cycle strain damage accumulation near the crack tip along the cracking direction and the Newman–Raju formula is developed. The crack is regarded as a sharp notch with a small curvature radius and the process zone is assumed to be the size of cyclic plastic zone. The modified Hutchinson, Rice and Rosengren (HRR formulations are used in the presented study. Assuming that the shape of surface crack front is controlled by two critical points: the deepest point and the surface point. The theoretical model is applied to semi-elliptic surface cracked Al 7075-T6 alloy plate under cyclic loading, and five different initial crack shapes are discussed in present study. Good agreement between experimental and theoretical results is obtained.

Beam instabilities are among the main limitations in building higher intensity accelerators. Having a good impedance model for every accelerators is necessary in order to build components that minimize the probability of instabilities caused by the interaction beam-environment and to understand what piece to change in case of intensity increasing. Most of accelerator components have their impedance simulated with finite elements method (using softwares like CST Studio), but simple components such as circular or flat pipes are modeled analytically, with a decreasing computation time and an increasing precision compared to their simulated model. Elliptical beam pipes, while being a simple component present in some accelerators, still misses a good analytical model working for the hole range of velocities and frequencies. In this report, we present a general framework to study the impedance of elliptical pipes analytically. We developed a model for both longitudinal and transverse impedance, first in the case of...

This paper analyzes the performance of an Electric Solar Wind Sail for generating and maintaining an elliptic, heliocentric, displaced non-Keplerian orbit. In this sense, this paper extends and completes recent studies regarding the performances of an Electric Solar Wind Sail that covers a circular, heliocentric, displaced orbit of given characteristics. The paper presents the general equations that describe the elliptic orbit maintenance in terms of both spacecraft attitude and performance requirements, when a refined thrust model (recently proposed for the preliminary mission design) is taken into account. In particular, the paper also discusses some practical applications on particular mission scenarios in which an analytic solution of the governing equations has been found.

It is not surprising that the baryonic material inside the more compact halos will tend to form a more compact, luminous elliptical. What needs to be explained is the difference in the value of the spin parameter (lambda). It might be tempting to speculate that more compact, dense halos have systematically smaller values of lambda. Such an effect is predicted by linear calculations. Our simulations show that it may exist but it appears to be too small compared to the random scatter of the values of lambda and rho to be decisive. It is more likely that the baryonic material has initially similar lambda both in the future spirals and elliptical but compact halos damp out the lambda of the dissipative, baryonic material more readily

We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.

An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.

We demonstrate for the first time an intensitymodulated direct-detection link using four states of polarization. The four data-independent tributaries are each assigned distinct states of polarization to enable the receiver to separate the signals. Polarization rotation due to propagation over op...

Three methods of polarized radioactive nuclei beam production: a) a method nuclear interaction of the non-polarized or polarized charged projectiles with target nuclei; b) a method of polarization of stopped reaction radioactive products in a special polarized ion source with than following acceleration; c) a polarization of radioactive nuclei circulating in a storage ring are considered. Possible life times of the radioactive ions for these methods are determined. General schemes of the polarization method realizations and depolarization problems are discussed

The application of a global optimization procedure to the detection of buried inhomogeneities is studied in the present paper. The object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. An efficient recursive analytical procedure is used for the forward scattering computation. A functional is constructed in which the field is expressed in series solution of Mathieu functions. Starting by the input scattered data, the iterative minimiza...

In this conference the effect of ellipticity and triangularity will be analyzed for axisymmetric tokamak in the collisional regime. Analytic forms for the magnetic field cross sections are taken from those derived recently by other authors [1,2]. Analytical results can be obtained in elliptic plasmas with triangularity by using an special system of tokamak coordinates recently published [3-5]. Our results show that triangularities smaller than 0.6, increases confinement for ellipticities in the range 1.2 to 2. This behavior happens for negative and positive triangularities; however this effect is stronger for positive than for negative triangularities. The maximum diffusion velocity is not obtained for zero triangularity, but for small negative triangularities. Ellipticity is also very important in confinement, but the effect of triangularity seems to be more important. High electric inductive field increases confinement, though this field is difficult to modify once the tokamak has been built. The analytic form of the current produced by this field is like that of a weak Ware pinch with an additional factor, which weakens the effect by an order of magnitude. The dependence of the triangularity effect with the Shafranov shift is also analyzed. References 1. - L. L. Lao, S. P. Hirshman, and R. M. Wieland, Phys. Fluids 24, 1431 (1981) 2. - G. O. Ludwig, Plasma Physics Controlled Fusion 37, 633 (1995) 3. - P. Martin, Phys. Plasmas 7, 2915 (2000) 4. - P. Martin, M. G. Haines and E. Castro, Phys. Plasmas 12, 082506 (2005) 5. - P. Martin, E. Castro and M. G. Haines, Phys. Plasmas 12, 102505 (2005)

We employed Poincar\\'e return mappings for a parameter interval to an exemplary elliptic bursting model, the FitzHugh-Nagumo-Rinzel model. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally, mixed-mode oscillations and quiescence in the FitzHugh-Nagumo-Rinzel model. We illustrate the wealth of information, qualitative and quantitati...

Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig

Full Text Available Nonsmooth-critical-point theory is applied in proving multiplicity results for the quasilinear symmetric elliptic system $$ -sum_{i,j=1}^{n}D_j(a^{k}_{ij}(x,uD_iu_k+ {1over 2}sum_{i,j=1}^{n}sum_{h=1}^N D_{s_k}a^{h}_{ij}(x,uD_iu_hD_ju_h=g_k(x,u,, $$ for $k=1,..,N$.

Full Text Available We establish the existence and multiplicity of weak solutions of a problem involving a uniformly convex elliptic operator in divergence form. We find one nontrivial solution by the mountain pass lemma, when the nonlinearity has a $(p-1$-superlinear growth at infinity, and two nontrivial solutions by minimization and mountain pass when the nonlinear term has a $(p-1$-sublinear growth at infinity.

Intersecting bore geometries are used in a number of industrial applications including heavy-walled pressure vessels containing oil holes for lubrication, ports for valves and fluid ends of reciprocating pumps. The bore intersection location is a stress concentration point where the maximum hoop stress can be many times the fluid pressure in the bores. Intersecting circular holes in heavy-walled cylinders and rectangular blocks have been extensively investigated. Specifically, stress/pressure concentration curves for intersecting circular bores in rectangular blocks were presented by Sorem et al. [Sorem JR, Shadley JR, Tipton SM. Design curves for maximum stresses in blocks containing pressurized bore intersections. ASME J Mech Des 1990; 113: 427-31.]. However, stress/pressure concentrations due to intersecting elliptic bores have not been broadly investigated. With the availability of computer numerical control (CNC) machinery, bores with elliptic crosssection can be produced with relative ease. In this paper, hoop stress concentration ratios are developed for elliptic crossbores in rectangular blocks. Results indicate that introducing elliptic crossbores, rather than circular ones, significantly reduces the hoop stress concentration factor at the crossbore intersection. Also, the presence of intersecting crossbores has a major effect on the fatigue life of pressure vessels [Badr EA, Sorem JR, Jr Tipton SM. Evaluation of the autofrettage effect on fatigue lives of steel blocks with crossbores using a statistical and a strain-based method. ASTM J Test Eval 2000; 28: 181-8.] and the reduction of hoop stress concentration is expected to enhance the fatigue life of pressure vessels containing crossbores

Computational aspects of the box domain decomposition (DD) method for solving boundary value problems in an unbounded domain are discussed. A new variant of the DD-method for elliptic problems in unbounded domains is suggested. It is based on the partitioning of an unbounded domain adapted to the given asymptotic decay of an unknown function at infinity. The comparison of computational expenditures is given for boundary integral method and the suggested DD-algorithm. 29 refs.; 2 figs.; 2 tabs

Full Text Available This article shows the existence of solutions to the nonlinear elliptic problem $A(u=f$ in Orlicz-Sobolev spaces with a measure valued right-hand side, where $A(u=-mathop{ m div}a(x,u, abla u$ is a Leray-Lions operator defined on a subset of $W_{0}^{1}L_{M}(Omega$, with general $M$.

We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results

In order to remove singularities, Riemann used a well-known device of taking the odd part (3.2) or an alternate sum (3.3) to be stated in §3. In §2 of this note we shall reveal that the limit values of elliptic modular functions in Riemann's fragment II evaluated by the differences of polyloga- rithm function l1(x) of order 1 (cf.

In many applications polar cranes have to be repeatedly positioned with high accuracy. A guidance system is disclosed which has two pairs of guides. Each guide consists of two rollers carried by a sheave rotatable mounted on the crane bridge, the rollers being locatable one on each side of a guideway, e.g. the circular track on which the bridge runs. The pairs of guides are interconnected by respective rope loops which pass around and are locked to the respective pairs of sheaves in such a manner that movement of one guide results in equal movement of the other guide in a sense to maintain the repeatability of positioning of the centre of the bridge. A hydraulically-linked guide system is also described. (author)

An understanding of all factors influencing plant growth in a nursery environment is needed for the successful growth and production of high-quality container plants. Propagation structures modify the atmospheric conditions of temperature, light, and relative humidity. Native plant nurseries are different from typical horticultural nurseries because plants must be...

A rigorous comparison of power balance fluxes and turbulent model fluxes requires the propagation of uncertainties in the kinetic profiles and their derivatives. Making extensive use of the python uncertainties package, the OMFIT framework has been used to propagate covariant uncertainties to provide an uncertainty in the power balance calculation from the ONETWO code, as well as through the turbulent fluxes calculated by the TGLF code. The covariant uncertainties arise from fitting 1D (constant on flux surface) density and temperature profiles and associated random errors with parameterized functions such as a modified tanh. The power balance and model fluxes can then be compared with quantification of the uncertainties. No effort is made at propagating systematic errors. A case study will be shown for the effects of resonant magnetic perturbations on the kinetic profiles and fluxes at the top of the pedestal. A separate attempt at modeling the random errors with Monte Carlo sampling will be compared to the method of propagating the fitting function parameter covariant uncertainties. Work supported by US DOE under DE-FC02-04ER54698, DE-FG2-95ER-54309, DE-SC 0012656.

An analog of the j = 1/2 Feynman-Dyson propagator is presented in the framework of the j = 1 Weinberg's theory. The basis for this construction is the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations. (orig.)

This paper discusses the question of tropical cyclone propagation or why the average tropical cyclone moves 1-2 m/s faster and usually 10-20 deg to the left of its surrounding (or 5-7 deg radius) deep layer (850-300 mb) steering current...